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WhatIs-L

L L is a high-level, open-source, general-purpose and system programming language which emphasizes readability, simplicity, extensibility, conciseness and performance. The L compiler features native code generation through LLVM, and is fully documented in a literate programming style. The language and compiler are usable, but are under heavy development as new features are being implemented.
L1-Norm Batch Normalization
(L1BN)
Batch Normalization (BN) has been proven to be quite effective at accelerating and improving the training of deep neural networks (DNNs). However, BN brings additional computation, consumes more memory and generally slows down the training process by a large margin, which aggravates the training effort. Furthermore, the nonlinear square and root operations in BN also impede the low bit-width quantization techniques, which draws much attention in deep learning hardware community. In this work, we propose an L1-norm BN (L1BN) with only linear operations in both the forward and the backward propagations during training. L1BN is shown to be approximately equivalent to the original L2-norm BN (L2BN) by multiplying a scaling factor. Experiments on various convolutional neural networks (CNNs) and generative adversarial networks (GANs) reveal that L1BN maintains almost the same accuracies and convergence rates compared to L2BN but with higher computational efficiency. On FPGA platform, the proposed signum and absolute operations in L1BN can achieve 1.5$\times$ speedup and save 50\% power consumption, compared with the original costly square and root operations, respectively. This hardware-friendly normalization method not only surpasses L2BN in speed, but also simplify the hardware design of ASIC accelerators with higher energy efficiency. Last but not the least, L1BN promises a fully quantized training of DNNs, which is crucial to future adaptive terminal devices.
L1-Norm Kernel PCA We present the first model and algorithm for L1-norm kernel PCA. While L2-norm kernel PCA has been widely studied, there has been no work on L1-norm kernel PCA. For this non-convex and non-smooth problem, we offer geometric understandings through reformulations and present an efficient algorithm where the kernel trick is applicable. To attest the efficiency of the algorithm, we provide a convergence analysis including linear rate of convergence. Moreover, we prove that the output of our algorithm is a local optimal solution to the L1-norm kernel PCA problem. We also numerically show its robustness when extracting principal components in the presence of influential outliers, as well as its runtime comparability to L2-norm kernel PCA. Lastly, we introduce its application to outlier detection and show that the L1-norm kernel PCA based model outperforms especially for high dimensional data.
L1-Penalized Censored Gaussian Graphical Model Graphical lasso is one of the most used estimators for inferring genetic networks. Despite its diffusion, there are several fields in applied research where the limits of detection of modern measurement technologies make the use of this estimator theoretically unfounded, even when the assumption of a multivariate Gaussian distribution is satisfied. Typical examples are data generated by polymerase chain reactions and flow cytometer. The combination of censoring and high-dimensionality make inference of the underlying genetic networks from these data very challenging. In this paper we propose an $\ell_1$-penalized Gaussian graphical model for censored data and derive two EM-like algorithms for inference. By an extensive simulation study, we evaluate the computational efficiency of the proposed algorithms and show that our proposal overcomes existing competitors when censored data are available. We apply the proposed method to gene expression data coming from microfluidic RT-qPCR technology in order to make inference on the regulatory mechanisms of blood development.
L2-Nonexpansive Neural Network This paper proposes a class of well-conditioned neural networks in which a unit amount of change in the inputs causes at most a unit amount of change in the outputs or any of the internal layers. We develop the known methodology of controlling Lipschitz constants to realize its full potential in maximizing robustness: our linear and convolution layers subsume those in the previous Parseval networks as a special case and allow greater degrees of freedom; aggregation, pooling, splitting and other operators are adapted in new ways, and a new loss function is proposed, all for the purpose of improving robustness. With MNIST and CIFAR-10 classifiers, we demonstrate a number of advantages. Without needing any adversarial training, the proposed classifiers exceed the state of the art in robustness against white-box L2-bounded adversarial attacks. Their outputs are quantitatively more meaningful than ordinary networks and indicate levels of confidence. They are also free of exploding gradients, among other desirable properties.
Label Augmentation A major impediment to the application of deep learning to real-world problems is the scarcity of labeled data. Small training sets are in fact of no use to deep networks as, due to the large number of trainable parameters, they will very likely be subject to overfitting phenomena. On the other hand, the increment of the training set size through further manual or semi-automatic labellings can be costly, if not possible at times. Thus, the standard techniques to address this issue are transfer learning and data augmentation, which consists of applying some sort of ‘transformation’ to existing labeled instances to let the training set grow in size. Although this approach works well in applications such as image classification, where it is relatively simple to design suitable transformation operators, it is not obvious how to apply it in more structured scenarios. Motivated by the observation that in virtually all application domains it is easy to obtain unlabeled data, in this paper we take a different perspective and propose a \emph{label augmentation} approach. We start from a small, curated labeled dataset and let the labels propagate through a larger set of unlabeled data using graph transduction techniques. This allows us to naturally use (second-order) similarity information which resides in the data, a source of information which is typically neglected by standard augmentation techniques. In particular, we show that by using known game theoretic transductive processes we can create larger and accurate enough labeled datasets which use results in better trained neural networks. Preliminary experiments are reported which demonstrate a consistent improvement over standard image classification datasets.
Label Embedding Network We propose a method, called Label Embedding Network, which can learn label representation (label embedding) during the training process of deep networks. With the proposed method, the label embedding is adaptively and automatically learned through back propagation. The original one-hot represented loss function is converted into a new loss function with soft distributions, such that the originally unrelated labels have continuous interactions with each other during the training process. As a result, the trained model can achieve substantially higher accuracy and with faster convergence speed. Experimental results based on competitive tasks demonstrate the effectiveness of the proposed method, and the learned label embedding is reasonable and interpretable. The proposed method achieves comparable or even better results than the state-of-the-art systems. The source code is available at \url{https://…/LabelEmb}.
Labeled Latent Dirichlet Allocation
(LLDA)
Labeled Latent Dirichlet Allocation (LLDA) is an extension of the standard unsupervised Latent Dirichlet Allocation (LDA) algorithm, to address multi-label learning tasks. Previous work has shown it to perform in par with other state-of-the-art multi-label methods. Nonetheless, with increasing label sets sizes LLDA encounters scalability issues. In this work, we introduce Subset LLDA, a simple variant of the standard LLDA algorithm, that not only can effectively scale up to problems with hundreds of thousands of labels but also improves over the LLDA state-of-the-art. We conduct extensive experiments on eight data sets, with label sets sizes ranging from hundreds to hundreds of thousands, comparing our proposed algorithm with the previously proposed LLDA algorithms (Prior–LDA, Dep–LDA), as well as the state of the art in extreme multi-label classification. The results show a steady advantage of our method over the other LLDA algorithms and competitive results compared to the extreme multi-label classification algorithms.
Laconic We motivate a method for transparently identifying ineffectual computations in unmodified Deep Learning models and without affecting accuracy. Specifically, we show that if we decompose multiplications down to the bit level the amount of work performed during inference for image classification models can be consistently reduced by two orders of magnitude. In the best case studied of a sparse variant of AlexNet, this approach can ideally reduce computation work by more than 500x. We present Laconic a hardware accelerator that implements this approach to improve execution time, and energy efficiency for inference with Deep Learning Networks. Laconic judiciously gives up some of the work reduction potential to yield a low-cost, simple, and energy efficient design that outperforms other state-of-the-art accelerators. For example, a Laconic configuration that uses a weight memory interface with just 128 wires outperforms a conventional accelerator with a 2K-wire weight memory interface by 2.3x on average while being 2.13x more energy efficient on average. A Laconic configuration that uses a 1K-wire weight memory interface, outperforms the 2K-wire conventional accelerator by 15.4x and is 1.95x more energy efficient. Laconic does not require but rewards advances in model design such as a reduction in precision, the use of alternate numeric representations that reduce the number of bits that are ‘1’, or an increase in weight or activation sparsity.
LAD Regression
Ladder The organizer of a machine learning competition faces the problem of maintaining an accurate leaderboard that faithfully represents the quality of the best submission of each competing team. What makes this estimation problem particularly challenging is its sequential and adaptive nature. As participants are allowed to repeatedly evaluate their submissions on the leaderboard, they may begin to overfit to the holdout data that supports the leaderboard. Few theoretical results give actionable advice on how to design a reliable leaderboard. Existing approaches therefore often resort to poorly understood heuristics such as limiting the bit precision of answers and the rate of re-submission. In this work, we introduce a notion of leaderboard accuracy tailored to the format of a competition. We introduce a natural algorithm called the Ladder and demonstrate that it simultaneously supports strong theoretical guarantees in a fully adaptive model of estimation, withstands practical adversarial attacks, and achieves high utility on real submission files from an actual competition hosted by Kaggle.
Lagrange Multiplier In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints.
Lagrange Policy Gradient Most algorithms for reinforcement learning work by estimating action-value functions. Here we present a method that uses Lagrange multipliers, the costate equation, and multilayer neural networks to compute policy gradients. We show that this method can find solutions to time-optimal control problems, driving nonlinear mechanical systems quickly to a target configuration. On these tasks its performance is comparable to that of deep deterministic policy gradient, a recent action-value method.
Lambda Architecture Lambda Architecture proposes a simpler, elegant paradigm that is designed to tame complexity while being able to store and effectively process large amounts of data. The Lambda Architecture was originally presented by Nathan Marz, who is well known in the big data community for his work on the Storm project.
Lambda Architecture
Lambda Architecture
LambdaMART At a high level, LambdaMART is an algorithm that uses gradient boosting to directly optimize Learning to Rank specific cost functions such as NDCG.
Lambert W Function In mathematics, the Lambert W function, also called the omega function or product logarithm, is a set of functions, namely the branches of the inverse relation of the function z = f(W) = We^W where e^W is the exponential function and W is any complex number. In other words, the defining equation for W(z) is: z = W(z)e^{W(z)} for any complex number z.
http://…/LambertW-Function.html
lamW
Lanczos Latent Factor Recommender
(LLFR)
The purpose if this master’s thesis is to study and develop a new algorithmic framework for Collaborative Filtering to produce recommendations in the top-N recommendation problem. Thus, we propose Lanczos Latent Factor Recommender (LLFR); a novel ‘big data friendly’ collaborative filtering algorithm for top-N recommendation. Using a computationally efficient Lanczos-based procedure, LLFR builds a low dimensional item similarity model, that can be readily exploited to produce personalized ranking vectors over the item space. A number of experiments on real datasets indicate that LLFR outperforms other state-of-the-art top-N recommendation methods from a computational as well as a qualitative perspective. Our experimental results also show that its relative performance gains, compared to competing methods, increase as the data get sparser, as in the Cold Start Problem. More specifically, this is true both when the sparsity is generalized – as in the New Community Problem, a very common problem faced by real recommender systems in their beginning stages, when there is not sufficient number of ratings for the collaborative filtering algorithms to uncover similarities between items or users – and in the very interesting case where the sparsity is localized in a small fraction of the dataset – as in the New Users Problem, where new users are introduced to the system, they have not rated many items and thus, the CF algorithm can not make reliable personalized recommendations yet.
Lanczos Method The Lanczos algorithm is a direct algorithm devised by Cornelius Lanczos that is an adaptation of power methods to find the most useful eigenvalues and eigenvectors of an n t h {\displaystyle n^{th}} n^{{th}} order linear system with a limited number of operations, m {\displaystyle m} m, where m {\displaystyle m} m is much smaller than n {\displaystyle n} n. Although computationally efficient in principle, the method as initially formulated was not useful, due to its numerical instability. In 1970, Ojalvo and Newman showed how to make the method numerically stable and applied it to the solution of very large engineering structures subjected to dynamic loading. This was achieved using a method for purifying the vectors to any degree of accuracy, which when not performed, produced a series of vectors that were highly contaminated by those associated with the lowest natural frequencies. In their original work, these authors also suggested how to select a starting vector (i.e. use a random number generator to select each element of the starting vector) and suggested an empirically determined method for determining m {\displaystyle m} m, the reduced number of vectors (i.e. it should be selected to be approximately 1 ½ times the number of accurate eigenvalues desired). Soon thereafter their work was followed by Paige who also provided an error analysis. In 1988, Ojalvo produced a more detailed history of this algorithm and an efficient eigenvalue error test. Currently, the method is widely used in a variety of technical fields and has seen a number of variations.
LanczOs Variance Estimates
(LOVE)
One of the most compelling features of Gaussian process (GP) regression is its ability to provide well calibrated posterior distributions. Recent advances in inducing point methods have drastically sped up marginal likelihood and posterior mean computations, leaving posterior covariance estimation and sampling as the remaining computational bottlenecks. In this paper we address this shortcoming by using the Lanczos decomposition algorithm to rapidly approximate the predictive covariance matrix. Our approach, which we refer to as LOVE (LanczOs Variance Estimates), substantially reduces the time and space complexity over any previous method. In practice, it can compute predictive covariances up to 2,000 times faster and draw samples 18,000 time faster than existing methods, all without sacrificing accuracy.
Landmark Retracing Network
(LRN)
Since convolutional neural network (CNN) lacks an inherent mechanism to handle large scale variations, we always need to compute feature maps multiple times for multi-scale object detection, which has the bottleneck of computational cost in practice. To address this, we devise a recurrent scale approximation (RSA) to compute feature map once only, and only through this map can we approximate the rest maps on other levels. At the core of RSA is the recursive rolling out mechanism: given an initial map on a particular scale, it generates the prediction on a smaller scale that is half the size of input. To further increase efficiency and accuracy, we (a): design a scale-forecast network to globally predict potential scales in the image since there is no need to compute maps on all levels of the pyramid. (b): propose a landmark retracing network (LRN) to retrace back locations of the regressed landmarks and generate a confidence score for each landmark; LRN can effectively alleviate false positives due to the accumulated error in RSA. The whole system could be trained end-to-end in a unified CNN framework. Experiments demonstrate that our proposed algorithm is superior against state-of-the-arts on face detection benchmarks and achieves comparable results for generic proposal generation. The source code of RSA is available at github.com/sciencefans/RSA-for-object-detection.
Langevin Monte Carlo
Language Model A statistical language model assigns a probability to a sequence of m words by means of a probability distribution. Language modeling is used in many natural language processing applications such as speech recognition, machine translation, part-of-speech tagging, parsing and information retrieval.
Laplacian Power Network Deep Neural Networks often suffer from lack of robustness to adversarial noise. To mitigate this drawback, authors have proposed different approaches, such as adding regularizers or training using adversarial examples. In this paper we propose a new regularizer built upon the Laplacian of similarity graphs obtained from the representation of training data at each intermediate representation. This regularizer penalizes large changes (across consecutive layers in the architecture) in the distance between examples of different classes. We provide theoretical justification for this regularizer and demonstrate its effectiveness when facing adversarial noise on classical supervised learning vision datasets.
Large Deviation Principles We establish the Large Deviation Principles for a topological Markov shift on a countably infinite number of alphabets which satisfies a strong combinatorial assumption called ‘finite primitiveness’ by Mauldin $\&$ Urba\’nski. More precisely, we assume the existence of a Gibbs measure for a potential $\phi$ in the sense of Bowen, and prove the level-2 Large Deviation Principles for the distribution of Birkhoff averages under the Gibbs measure, as well as that of weighted periodic points and iterated pre-images. The rate function is in common, written with the pressure and the free energy associated with the potential $\phi$. The Gibbs measure is not assumed to be an equilibrium state for the potential $\phi$, nor is assumed the existence of an equilibrium state. We provide a sufficient condition for minimizers of the rate function to be equilibrium states. We apply our results to the Gauss transformation and obtain a global limit theorem on the frequency of digits in the regular continued fraction expansion.
Large Margin Deep Network We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks. However, most large margin algorithms are applicable only to shallow models with a preset feature representation; and conventional margin methods for neural networks only enforce margin at the output layer. Such methods are therefore not well suited for deep networks. In this work, we propose a novel loss function to impose a margin on any chosen set of layers of a deep network (including input and hidden layers). Our formulation allows choosing any norm on the metric measuring the margin. We demonstrate that the decision boundary obtained by our loss has nice properties compared to standard classification loss functions. Specifically, we show improved empirical results on the MNIST, CIFAR-10 and ImageNet datasets on multiple tasks: generalization from small training sets, corrupted labels, and robustness against adversarial perturbations. The resulting loss is general and complementary to existing data augmentation (such as random/adversarial input transform) and regularization techniques (such as weight decay, dropout, and batch norm).
Large Vocabulary Continuous Speech Recognition System
(LVCSR)
The search problem in LVCSR can be simply stated: find the most probable sequence of words given a sequence of acoustic observations, an acoustic model and a language model. This is a demanding problem since word boundary information is not available in continuous speech and each word in the dictionary may be hypothesized to start at each frame of acoustic data. The problem is further complicated by the vocabulary size (typically 65,000 words) and the structure imposed on the search space by the language model. Direct evaluation of all the possible word sequences is impossible (given the large vocabulary) and an efficient search algorithm will consider only a very small subset of all possible utterance models. Typically, the effective size of the search space is reduced through pruning of unlikely hypotheses and/or the elimination of repeated computations.
Large-Scale Information Network Embedding
(LINE)
This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes. In this paper, we propose a novel network embedding method called the ‘LINE,’ which is suitable for arbitrary types of information networks: undirected, directed, and/or weighted. The method optimizes a carefully designed objective function that preserves both the local and global network structures. An edge-sampling algorithm is proposed that addresses the limitation of the classical stochastic gradient descent and improves both the effectiveness and the efficiency of the inference. Empirical experiments prove the effectiveness of the LINE on a variety of real-world information networks, including language networks, social networks, and citation networks. The algorithm is very efficient, which is able to learn the embedding of a network with millions of vertices and billions of edges in a few hours on a typical single machine. The source code of the LINE is available online.
Largest Gaps In this paper, the algorithm $Largest$ $Gaps$ is introduced, for simultaneously clustering both rows and columns of a matrix to form homogeneous blocks. The definition of clustering is model-based: clusters and data are generated under the Latent Block Model. In comparison with algorithms designed for this model, the major advantage of the $Largest$ $Gaps$ algorithm is to cluster using only some marginals of the matrix, the size of which is much smaller than the whole matrix. The procedure is linear with respect to the number of entries and thus much faster than the classical algorithms. It simultaneously selects the number of classes as well, and the estimation of the parameters is then made very easily once the classification is obtained. Moreover, the paper proves the procedure to be consistent under the LBM, and it illustrates the statistical performance with some numerical experiments.
Lasagne In this work we propose Lasagne, a methodology to learn locality and structure aware graph node embeddings in an unsupervised way. In particular, we show that the performance of existing random-walk based approaches depends strongly on the structural properties of the graph, e.g., the size of the graph, whether the graph has a flat or upward-sloping Network Community Profile (NCP), whether the graph is expander-like, whether the classes of interest are more k-core-like or more peripheral, etc. For larger graphs with flat NCPs that are strongly expander-like, existing methods lead to random walks that expand rapidly, touching many dissimilar nodes, thereby leading to lower-quality vector representations that are less useful for downstream tasks. Rather than relying on global random walks or neighbors within fixed hop distances, Lasagne exploits strongly local Approximate Personalized PageRank stationary distributions to more precisely engineer local information into node embeddings. This leads, in particular, to more meaningful and more useful vector representations of nodes in poorly-structured graphs. We show that Lasagne leads to significant improvement in downstream multi-label classification for larger graphs with flat NCPs, that it is comparable for smaller graphs with upward-sloping NCPs, and that is comparable to existing methods for link prediction tasks.
Lasso Penalized Sparse Asymmetric Least Squares
(SALES)
SALES
Lasso Regression
Lassoing Eigenvalues
(elasso)
The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of non-smooth penalty functions for the sample covariance matrix, and demonstrate how this method results in a grouping of the estimated eigenvalues. We refer to this method as ‘lassoing eigenvalues’ or as the ‘elasso’.
Last Observation Projection
LaSVM
(LaSVM)
LASVM is an approximate SVM solver that uses online approximation. It reaches accuracies similar to that of a real SVM after performing a single sequential pass through the training examples. Further benefits can be achieved using selective sampling techniques to choose which example should be considered next. As show in the graph, LASVM requires considerably less memory than a regular SVM solver. This becomes a considerable speed advantage for large training sets. In fact LASVM has been used to train a 10 class SVM classifier with 8 million examples on a single processor.
lasvmR
Latent Association Mining in Binary Data
(LAMB)
We consider the problem of identifying groups of mutually associated variables in moderate or high dimensional data. In many cases, ordinary Pearson correlation provides useful information concerning the linear relationship between variables. However, for binary data, ordinary correlation may lose power and may lack interpretability. In this paper, we develop and investigate a new method called Latent Association Mining in Binary Data (LAMB). The LAMB method is built on the assumption that the binary observations represent a random thresholding of a latent continuous variable that may have a complex correlation structure. We consider a new measure of association, latent correlation, that is designed to assess association in the underlying continuous variable, without bias due to the mediating effects of the thresholding procedure. The full LAMB procedure makes use of iterative hypothesis testing to identify groups of latently correlated variables. LAMB is shown to improve power over existing methods in simulated settings, to be computationally efficient for large datasets, and to uncover new meaningful results from common real data types.
Latent Attention Network Deep neural networks are able to solve tasks across a variety of domains and modalities of data. Despite many empirical successes, we lack the ability to clearly understand and interpret the learned internal mechanisms that contribute to such effective behaviors or, more critically, failure modes. In this work, we present a general method for visualizing an arbitrary neural network’s inner mechanisms and their power and limitations. Our dataset-centric method produces visualizations of how a trained network attends to components of its inputs. The computed ‘attention masks’ support improved interpretability by highlighting which input attributes are critical in determining output. We demonstrate the effectiveness of our framework on a variety of deep neural network architectures in domains from computer vision, natural language processing, and reinforcement learning. The primary contribution of our approach is an interpretable visualization of attention that provides unique insights into the network’s underlying decision-making process irrespective of the data modality.
Latent Autoregressive Count Models See Pedeli and Varin (2018) <arXiv:1805.10865> for details.
lacm
Latent Class Analysis
(LCA)
Latent class analysis (LCA) identifies unobservable subgroups within a population.
Latent Class Model
(LCM)
In statistics, a latent class model (LCM) relates a set of observed (usually discrete) multivariate variables to a set of latent variables. It is a type of latent variable model. It is called a latent class model because the latent variable is discrete. A class is characterized by a pattern of conditional probabilities that indicate the chance that variables take on certain values. Latent Class Analysis (LCA) is a subset of structural equation modeling, used to find groups or subtypes of cases in multivariate categorical data. These subtypes are called “latent classes”. Confronted with a situation as follows, a researcher might choose to use LCA to understand the data: Imagine that symptoms a-d have been measured in a range of patients with diseases X Y and Z, and that disease X is associated with the presence of symptoms a, b, and c, disease Y with symptoms b, c, d, and disease Z with symptoms a, c and d. The LCA will attempt to detect the presence of latent classes (the disease entities), creating patterns of association in the symptoms. As in factor analysis, the LCA can also be used to classify case according to their maximum likelihood class membership. Because the criterion for solving the LCA is to achieve latent classes within which there is no longer any association of one symptom with another (because the class is the disease which causes their association, and the set of diseases a patient has (or class a case is a member of) causes the symptom association, the symptoms will be “conditionally independent”, i.e., conditional on class membership, they are no longer related.
Latent Constrained Correlation Filter
(LCCF)
Correlation filters are special classifiers designed for shift-invariant object recognition, which are robust to pattern distortions. The recent literature shows that combining a set of sub-filters trained based on a single or a small group of images obtains the best performance. The idea is equivalent to estimating variable distribution based on the data sampling (bagging), which can be interpreted as finding solutions (variable distribution approximation) directly from sampled data space. However, this methodology fails to account for the variations existed in the data. In this paper, we introduce an intermediate step — solution sampling — after the data sampling step to form a subspace, in which an optimal solution can be estimated. More specifically, we propose a new method, named latent constrained correlation filters (LCCF), by mapping the correlation filters to a given latent subspace, and develop a new learning framework in the latent subspace that embeds distribution-related constraints into the original problem. To solve the optimization problem, we introduce a subspace based alternating direction method of multipliers (SADMM), which is proven to converge at the saddle point. Our approach is successfully applied to three different tasks, including eye localization, car detection and object tracking. Extensive experiments demonstrate that LCCF outperforms the state-of-the-art methods. The source code will be publicly available. https://…/.
Latent Constraints Deep generative neural networks have proven effective at both conditional and unconditional modeling of complex data distributions. Conditional generation enables interactive control, but creating new controls often requires expensive retraining. In this paper, we develop a method to condition generation without retraining the model. By post-hoc learning latent constraints, value functions that identify regions in latent space that generate outputs with desired attributes, we can conditionally sample from these regions with gradient-based optimization or amortized actor functions. Combining attribute constraints with a universal ‘realism’ constraint, which enforces similarity to the data distribution, we generate realistic conditional images from an unconditional variational autoencoder. Further, using gradient-based optimization, we demonstrate identity-preserving transformations that make the minimal adjustment in latent space to modify the attributes of an image. Finally, with discrete sequences of musical notes, we demonstrate zero-shot conditional generation, learning latent constraints in the absence of labeled data or a differentiable reward function. Code with dedicated cloud instance has been made publicly available (https://goo.gl/STGMGx ).
Latent Dirichlet Allocation
(LDA)
In natural language processing, latent Dirichlet allocation (LDA) is a generative model that allows sets of observations to be explained by unobserved groups that explain why some parts of the data are similar. For example, if observations are words collected into documents, it posits that each document is a mixture of a small number of topics and that each word’s creation is attributable to one of the document’s topics. LDA is an example of a topic model and was first presented as a graphical model for topic discovery by David Blei, Andrew Ng, and Michael Jordan in 2003.
LDAvis
Latent Dirichlet allocation Gibbs Newton
(LDA-GN)
Hyper-parameters play a major role in the learning and inference process of latent Dirichlet allocation (LDA). In order to begin the LDA latent variables learning process, these hyper-parameters values need to be pre-determined. We propose an extension for LDA that we call ‘Latent Dirichlet allocation Gibbs Newton’ (LDA-GN), which places non-informative priors over these hyper-parameters and uses Gibbs sampling to learn appropriate values for them. At the heart of LDA-GN is our proposed ‘Gibbs-Newton’ algorithm, which is a new technique for learning the parameters of multivariate Polya distributions. We report Gibbs-Newton performance results compared with two prominent existing approaches to the latter task: Minka’s fixed-point iteration method and the Moments method. We then evaluate LDA-GN in two ways: (i) by comparing it with standard LDA in terms of the ability of the resulting topic models to generalize to unseen documents; (ii) by comparing it with standard LDA in its performance on a binary classification task.
Latent Embedding Optimization
(LEO)
Meta-Learning with Latent Embedding Optimization
Latent Factor Interpretation
(LFI)
Many machine learning systems utilize latent factors as internal representations for making predictions. However, since these latent factors are largely uninterpreted, predictions made using them are opaque. Collaborative filtering via matrix factorization is a prime example of such an algorithm that uses uninterpreted latent features, and yet has seen widespread adoption for many recommendation tasks. We present Latent Factor Interpretation (LFI), a method for interpreting models by leveraging interpretations of latent factors in terms of human-understandable features. The interpretation of latent factors can then replace the uninterpreted latent factors, resulting in a new model that expresses predictions in terms of interpretable features. This new model can then be interpreted using recently developed model explanation techniques. In this paper, we develop LFI for collaborative filtering based recommender systems, which are particularly challenging from an interpretation perspective. We illustrate the use of LFI interpretations on the MovieLens dataset demonstrating that latent factors can be predicted with enough accuracy for accurately replicating the predictions of the true model. Further, we demonstrate the accuracy of interpretations by applying the methodology to a collaborative recommender system using DB tropes and IMDB data and synthetic user preferences.
Latent Feature Relational Model
(LFRM)
We present a discriminative nonparametric latent feature relational model (LFRM) for link prediction to automatically infer the dimensionality of latent features. Under the generic RegBayes (regularized Bayesian inference) framework, we handily incorporate the prediction loss with probabilistic inference of a Bayesian model; set distinct regularization parameters for different types of links to handle the imbalance issue in real networks; and unify the analysis of both the smooth logistic log-loss and the piecewise linear hinge loss. For the nonconjugate posterior inference, we present a simple Gibbs sampler via data augmentation, without making restricting assumptions as done in variational methods. We further develop an approximate sampler using stochastic gradient Langevin dynamics to handle large networks with hundreds of thousands of entities and millions of links, orders of magnitude larger than what existing LFRM models can process. Extensive studies on various real networks show promising performance.
Latent Gaussian Process Regression We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary processes using stationary GP priors. The approach is built on extending the input space of a regression problem with a latent variable that is used to modulate the covariance function over the input space. We show how our approach can be used to model non-stationary processes but also how multi-modal or non-functional processes can be described where the input signal cannot fully disambiguate the output. We exemplify the approach on a set of synthetic data and provide results on real data from geostatistics.
Latent Order Logistic
(LOLOG)
Full probability models are critical for the statistical modeling of complex networks, and yet there are few general, flexible and widely applicable generative methods. We propose a new family of probability models motivated by the idea of network growth, which we call the Latent Order Logistic (LOLOG) model. LOLOG is a fully general framework capable of describing any probability distribution over graph configurations, though not all distributions are easily expressible or estimable as a LOLOG. We develop inferential procedures based on Monte Carlo Method of Moments, Generalized Method of Moments and variational inference. To show the flexibility of the model framework, we show how so-called scale-free networks can be modeled as LOLOGs via preferential attachment. The advantages of LOLOG in terms of avoidance of degeneracy, ease of sampling, and model flexibility are illustrated. Connections with the popular Exponential-family Random Graph model (ERGM) are also explored, and we find that they are identical in the case of dyadic independence. Finally, we apply the model to a social network of collaboration within a corporate law firm, a friendship network among adolescent students, and the friendship relations in an online social network.
Latent Profile Analysis
(LPA)
tidyLPA
Latent RANSAC We present a method that can evaluate a RANSAC hypothesis in constant time, i.e. independent of the size of the data. A key observation here is that correct hypotheses are tightly clustered together in the latent parameter domain. In a manner similar to the generalized Hough transform we seek to find this cluster, only that we need as few as two votes for a successful detection. Rapidly locating such pairs of similar hypotheses is made possible by adapting the recent ‘Random Grids’ range-search technique. We only perform the usual (costly) hypothesis verification stage upon the discovery of a close pair of hypotheses. We show that this event rarely happens for incorrect hypotheses, enabling a significant speedup of the RANSAC pipeline. The suggested approach is applied and tested on three robust estimation problems: camera localization, 3D rigid alignment and 2D-homography estimation. We perform rigorous testing on both synthetic and real datasets, demonstrating an improvement in efficiency without a compromise in accuracy. Furthermore, we achieve state-of-the-art 3D alignment results on the challenging ‘Redwood’ loop-closure challenge.
Latent Semantic Analysis
(LSA)
Latent semantic analysis (LSA) is a technique in natural language processing, in particular in vectorial semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms. LSA assumes that words that are close in meaning will occur in similar pieces of text. A matrix containing word counts per paragraph (rows represent unique words and columns represent each paragraph) is constructed from a large piece of text and a mathematical technique called singular value decomposition (SVD) is used to reduce the number of columns while preserving the similarity structure among rows. Words are then compared by taking the cosine of the angle between the two vectors formed by any two rows. Values close to 1 represent very similar words while values close to 0 represent very dissimilar words.
Latent Sequence Decompositions
(LSD)
We present the Latent Sequence Decompositions (LSD) framework. LSD decomposes sequences with variable lengthed output units as a function of both the input sequence and the output sequence. We present a training algorithm which samples valid extensions and an approximate decoding algorithm. We experiment with the Wall Street Journal speech recognition task. Our LSD model achieves 12.9% WER compared to a character baseline of 14.8% WER. When combined with a convolutional network on the encoder, we achieve 9.2% WER.
Latent Structure Analysis
(LSA)
latent structure analysis (LSA). LSA is a broad category that subsumes several individual methods, including latent class analysis (LCA) and latent trait analysis (LTA). The purpose of LSA is to infer, from observed variables (manifest variables), the structure of other, more fundamental variables that are not directly observed (latent variables). Both manifest variables and latent variables can be binary, nominal, ordered-categorical, or interval/continuous – leading to a large different combinations and different methods. For example, classical latent class analysis considers binary, nominal, or ordered-categorical manifest variables and nominal latent variables, and latent trait analysis considers binary or ordered-categorical variables and continuous latent variables.
Latent Structure Learning
(LSL)
lsl
Latent Trait Analysis
(LTA)
Latent Trait Analysis (LTA), a form of latent structure analysis (Lazarsfeld & Henry, 1968), is used for the analysis of categorical data. The simplest way to understand it is that LTA is form of factor analysis for binary (dichotomous) or ordered-category data. In the area of educational testing and psychological measurement, latent trait analysis is termed Item Response Theory (IRT). There is so much overlap between LTA and IRT that these terms are basically interchangeable.

ltm

Latent Transition Analysis
(LTA)
Latent transition analysis (LTA) and latent class analysis (LCA) are closely related methods. LCA identifies unobservable (latent) subgroups within a population based on individuals’ responses to multiple observed variables. LTA is an extension of LCA that uses longitudinal data to identify movement between the subgroups over time.
Latent Tree Learning “Latent Tree Models”
Latent Tree Models Latent tree models are graphical models defined on trees, in which only a subset of variables is observed. They were first discussed by Judea Pearl as tree-decomposable distributions to generalise star-decomposable distributions such as the latent class model. Latent tree models, or their submodels, are widely used in: phylogenetic analysis, network tomography, computer vision, causal modeling, and data clustering. They also contain other well-known classes of models like hidden Markov models, Brownian motion tree model, the Ising model on a tree, and many popular models used in phylogenetics. This article offers a concise introduction to the theory of latent tree models. We emphasise the role of tree metrics in the structural description of this model class, in designing learning algorithms, and in understanding fundamental limits of what and when can be learned.
Latent Tree Variational Autoencoder
(LTVAE)
Recently, deep learning based clustering methods are shown superior to traditional ones by jointly conducting representation learning and clustering. These methods rely on the assumptions that the number of clusters is known, and that there is one single partition over the data and all attributes define that partition. However, in real-world applications, prior knowledge of the number of clusters is usually unavailable and there are multiple ways to partition the data based on subsets of attributes. To resolve the issues, we propose latent tree variational autoencoder (LTVAE), which simultaneously performs representation learning and multidimensional clustering. LTVAE learns latent embeddings from data, discovers multi-facet clustering structures based on subsets of latent features, and automatically determines the number of clusters in each facet. Experiments show that the proposed method achieves state-of-the-art clustering performance and reals reasonable multifacet structures of the data.
Latent Truth Discovery
(LTD)
Latent truth discovery, LTD for short, refers to the problem of aggregating multiple claims from various sources in order to estimate the plausibility of statements about entities. In the absence of a ground truth, this problem is highly challenging, when some sources provide conflicting claims and others no claims at all.
Latent Variable Discovery Algorithm
(LatentSearch)
We consider the problem of discovering the simplest latent variable that can make two observed discrete variables conditionally independent. This problem has appeared in the literature as probabilistic latent semantic analysis (pLSA), and has connections to non-negative matrix factorization. When the simplicity of the variable is measured through its cardinality, we show that a solution to this latent variable discovery problem can be used to distinguish direct causal relations from spurious correlations among almost all joint distributions on simple causal graphs with two observed variables. Conjecturing a similar identifiability result holds with Shannon entropy, we study a loss function that trades-off between entropy of the latent variable and the conditional mutual information of the observed variables. We then propose a latent variable discovery algorithm — LatentSearch — and show that its stationary points are the stationary points of our loss function. We experimentally show that LatentSearch can indeed be used to distinguish direct causal relations from spurious correlations.
Latent Variable Mixture Model
(LVMM)
Latent variable mixture modeling (LVMM) is a flexible analytic tool that allows researchers to investigate questions about patterns of data and to determine the extent to which identified patterns relate to important variables. For example,
· Do patterns of co-occurring developmental and medical diagnoses influence the severity of pediatric feeding problems (Berlin, Lobato, Pinkos, Cerezo, & LeLeiko, 2011)?
· Do differential longitudinal trajectories of glycemic control exist among youth with type 1 diabetes (Helgeson et al., 2010)
· Do differential trajectories of adherence among youth newly diagnosed with epilepsy exist (Modi, Rausch, & Glauser, 2011), and if so,
· Do psychosocial and demographic variables predict these patterns?
· Do patterns of perceived stressors among youth with type 1 diabetes differentially affect glycemic control (Berlin, Rabideau, & Hains, 2012)?
http://…cgi?article=1093&context=famconfacpub
http://…/latent-variable-mixture-models-lvmm.html
Latent Variable Model A latent variable model is a statistical model that relates a set of variables (so-called manifest variables) to a set of latent variables. It is assumed that the responses on the indicators or manifest variables are the result of an individual’s position on the latent variable(s), and that the manifest variables have nothing in common after controlling for the latent variable (local independence). Different types of the latent variable model can be grouped according to whether the manifest and latent variables are categorical or continuous.
Latin Hypercube Design MOLHD
Latitude Nonnegative matrix factorization (NMF) is one of the most frequently-used matrix factorization models in data analysis. A significant reason to the popularity of NMF is its interpretability and the `parts of whole’ interpretation of its components. Recently, max-times, or subtropical, matrix factorization (SMF) has been introduced as an alternative model with equally interpretable `winner takes it all’ interpretation. In this paper we propose a new mixed linear–tropical model, and a new algorithm, called Latitude, that combines NMF and SMF, being able to smoothly alternate between the two. In our model, the data is modeled using the latent factors and latent parameters that control whether the factors are interpreted as NMF or SMF features, or their mixtures. We present an algorithm for our novel matrix factorization. Our experiments show that our algorithm improves over both baselines, and can yield interpretable results that reveal more of the latent structure than either NMF or SMF alone.
Lavaan Project The lavaan package is developed to provide useRs, researchers and teachers a free open-source, but commercial-quality package for latent variable modeling. You can use lavaan to estimate a large variety of multivariate statistical models, including path analysis, confirmatory factor analysis, structural equation modeling and growth curve models. The official reference to the lavaan package is the following paper: Yves Rosseel (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36. URL http://…/i02
lavaan,lavaan.shiny,lavaanPlot,blavaan
Law of Likelihood If hypothesis A implies that the probability that a random variable X takes the value x is pA(x), while hypothesis B implies that the probability is pB(x), then the observation X = x is evidence supporting A over B if and only if pA(x) > pB(x), and the likelihood ratio, pA(x)/ pB(x), measures the strength of that evidence.’
‘This says simply that if an event is more probable under hypothesis A than hypothesis B, then the occurrence of that event is evidence supporting A over B – the hypothesis that did the better job of predicting the event is better supported by its occurrence.’ Moreover, ‘the likelihood ratio, is the exact factor by which the probability ratio (ratio of priors in A and B) is changed.
Layer Trajectory LSTM
(ltLSTM)
It is popular to stack LSTM layers to get better modeling power, especially when large amount of training data is available. However, an LSTM-RNN with too many vanilla LSTM layers is very hard to train and there still exists the gradient vanishing issue if the network goes too deep. This issue can be partially solved by adding skip connections between layers, such as residual LSTM. In this paper, we propose a layer trajectory LSTM (ltLSTM) which builds a layer-LSTM using all the layer outputs from a standard multi-layer time-LSTM. This layer-LSTM scans the outputs from time-LSTMs, and uses the summarized layer trajectory information for final senone classification. The forward-propagation of time-LSTM and layer-LSTM can be handled in two separate threads in parallel so that the network computation time is the same as the standard time-LSTM. With a layer-LSTM running through layers, a gated path is provided from the output layer to the bottom layer, alleviating the gradient vanishing issue. Trained with 30 thousand hours of EN-US Microsoft internal data, the proposed ltLSTM performed significantly better than the standard multi-layer LSTM and residual LSTM, with up to 9.0% relative word error rate reduction across different tasks.
Layered Self-Organizing Map
(LSOM)
This paper defines a new learning architecture, Layered Self-Organizing Maps (LSOMs), that uses the SOM and supervised-SOM learning algorithms. The architecture is validated with the MNIST database of hand-written digit images. LSOMs are similar to convolutional neural nets (covnets) in the way they sample data, but different in the way they represent features and learn. LSOMs analyze (or generate) image patches with maps of exemplars determined by the SOM learning algorithm rather than feature maps from filter-banks learned via backprop. LSOMs provide an alternative to features derived from covnets. Multi-layer LSOMs are trained bottom-up, without the use of backprop and therefore may be of interest as a model of the visual cortex. The results show organization at multiple levels. The algorithm appears to be resource efficient in learning, classifying and generating images. Although LSOMs can be used for classification, their validation accuracy for these exploratory runs was well below the state of the art. The goal of this article is to define the architecture and display the structures resulting from its application to the MNIST images.
Layered Tree-Based Pipeline Optimization Tool
(Layered TPOT)
With the demand for machine learning increasing, so does the demand for tools which make it easier to use. Automated machine learning (AutoML) tools have been developed to address this need, such as the Tree-Based Pipeline Optimization Tool (TPOT) which uses genetic programming to build optimal pipelines. We introduce Layered TPOT, a modification to TPOT which aims to create pipelines equally good as the original, but in significantly less time. This approach evaluates candidate pipelines on increasingly large subsets of the data according to their fitness, using a modified evolutionary algorithm to allow for separate competition between pipelines trained on different sample sizes. Empirical evaluation shows that, on sufficiently large datasets, Layered TPOT indeed finds better models faster.
“Tree-Based Pipeline Optimization Tool”
Layer-Wise Relevance Propagation
(LRP)
Despite the tremendous achievements of deep convolutional neural networks~(CNNs) in most of computer vision tasks, understanding how they actually work remains a significant challenge. In this paper, we propose a novel two-step visualization method that aims to shed light on how deep CNNs recognize images and the objects therein. We start out with a layer-wise relevance propagation (LRP) step which estimates a pixel-wise relevance map over the input image. Following, we construct a context-aware saliency map from the LRP-generated map which predicts regions close to the foci of attention. We show that our algorithm clearly and concisely identifies the key pixels that contribute to the underlying neural network’s comprehension of images. Experimental results using the ILSVRC2012 validation dataset in conjunction with two well-established deep CNNs demonstrate that combining the LRP with the visual salience estimation can give great insight into how a CNNs model perceives and understands a presented scene, in relation to what it has learned in the prior training phase.
Layer-wIse-Semantic-Accumulation
(LISA)
Recurrent neural networks (RNNs) are temporal networks and cumulative in nature that have shown promising results in various natural language processing tasks. Despite their success, it still remains a challenge to understand their hidden behavior. In this work, we analyze and interpret the cumulative nature of RNN via a proposed technique named as Layer-wIse-Semantic-Accumulation (LISA) for explaining decisions and detecting the most likely (i.e., saliency) patterns that the network relies on while decision making. We demonstrate (1) LISA: ‘How an RNN accumulates or builds semantics during its sequential processing for a given text example and expected response’ (2) Example2pattern: ‘How the saliency patterns look like for each category in the data according to the network in decision making’. We analyse the sensitiveness of RNNs about different inputs to check the increase or decrease in prediction scores and further extract the saliency patterns learned by the network. We employ two relation classification datasets: SemEval 10 Task 8 and TAC KBP Slot Filling to explain RNN predictions via the LISA and example2pattern.
Lazy Bayesian Rules
(LBR)
The naive Bayesian classifier provides a simple and effective approach to classifier learning, but its attribute independence assumption is often violated in the real world. A number of approaches have sought to alleviate this problem. A Bayesian tree learning algorithm builds a decision tree, and generates a local naive Bayesian classifier at each leaf. The tests leading to a leaf can alleviate attribute inter-dependencies for the local naive Bayesian classifier. However, Bayesian tree learning still suffers from the small disjunct problem of tree learning. While inferred Bayesian trees demonstrate low average prediction error rates, there is reason to believe that error rates will be higher for those leaves with few training examples. This paper proposes the application of lazy learning techniques to Bayesian tree induction and presents the resulting lazy Bayesian rule learning algorithm, called Lbr. This algorithm can be justified by a variant of Bayes theorem which supports a weaker conditional attribute independence assumption than is required by naive Bayes. For each test example, it builds a most appropriate rule with a local naive Bayesian classifier as its consequent. It is demonstrated that the computational requirements of Lbr are reasonable in a wide cross-section of natural domains. Experiments with these domains show that, on average, this new algorithm obtains lower error rates significantly more often than the reverse in comparison to a naive Bayesian classifier, C4.5, a Bayesian tree learning algorithm, a constructive Bayesian classifier that eliminates attributes and constructs new attributes using Cartesian products of existing nominal attributes, and a lazy decision tree learning algorithm. It also outperforms, although the result is not statistically significant, a selective naive Bayesian classifier.
http://…/ZhengWebbTing99.pdf
http://…/CRPITV87Xie.pdf
Lazy Learning In artificial intelligence, lazy learning is a learning method in which generalization beyond the training data is delayed until a query is made to the system, as opposed to in eager learning, where the system tries to generalize the training data before receiving queries. The main advantage gained in employing a lazy learning method, such as Case based reasoning, is that the target function will be approximated locally, such as in the k-nearest neighbor algorithm. Because the target function is approximated locally for each query to the system, lazy learning systems can simultaneously solve multiple problems and deal successfully with changes in the problem domain. The disadvantages with lazy learning include the large space requirement to store the entire training dataset. Particularly noisy training data increases the case base unnecessarily, because no abstraction is made during the training phase. Another disadvantage is that lazy learning methods are usually slower to evaluate, though this is coupled with a faster training phase. Lazy classifiers are most useful for large datasets with few attributes.
Lazy Stochastic Principal Component Analysis
(Lazy SPCA)
Stochastic principal component analysis (SPCA) has become a popular dimensionality reduction strategy for large, high-dimensional datasets. We derive a simplified algorithm, called Lazy SPCA, which has reduced computational complexity and is better suited for large-scale distributed computation. We prove that SPCA and Lazy SPCA find the same approximations to the principal subspace, and that the pairwise distances between samples in the lower-dimensional space is invariant to whether SPCA is executed lazily or not. Empirical studies find downstream predictive performance to be identical for both methods, and superior to random projections, across a range of predictive models (linear regression, logistic lasso, and random forests). In our largest experiment with 4.6 million samples, Lazy SPCA reduced 43.7 hours of computation to 9.9 hours. Overall, Lazy SPCA relies exclusively on matrix multiplications, besides an operation on a small square matrix whose size depends only on the target dimensionality.
lda2vec Standard natural language processing (NLP) is a messy and difficult affair. It requires teaching a computer about English-specific word ambiguities as well as the hierarchical, sparse nature of words in sentences. At Stitch Fix, word vectors help computers learn from the raw text in customer notes. Our systems need to identify a medical professional when she writes that she ‘used to wear scrubs to work’, and distill ‘taking a trip’ into a Fix for vacation clothing. Applied appropriately, word vectors are dramatically more meaningful and more flexible than current techniques and let computers peer into text in a fundamentally new way. I’ll try to convince you that word vectors give us a simple and flexible platform for understanding text while speaking about word2vec, LDA, and introduce our hybrid algorithm lda2vec.
Leader Clustering Algorithm The leader clustering algorithm provides a means for clustering a set of data points. Unlike many other clustering algorithms it does not require the user to specify the number of clusters, but instead requires the approximate radius of a cluster as its primary tuning parameter. The package provides a fast implementation of this algorithm in n-dimensions using Lp-distances (with special cases for p=1,2, and infinity) as well as for spatial data using the Haversine formula, which takes latitude/longitude pairs as inputs and clusters based on great circle distances.
leaderCluster
Leaders and Subleaders Algorithm An efficient hierarchical clustering algorithm, suitable for large data sets is proposed for effective clustering and prototype selection for pattern classification. It is another simple and efficient technique which uses incremental clustering principles to generate a hierarchical structure for finding the subgroups/subclusters within each cluster. As an example, a two level clustering algorithm – Leaders-Subleaders, an extension of the leader algorithm is presented. Classification accuracy (CA) obtained using the representatives generated by the Leaders-Subleaders method is found to be better than that of using leaders as representatives. Even if more number of prototypes are generated, classification time is less as only a part of the hierarchical structure is searched.
Lead-like Recognizer
(LeadR)
A competitive baseline in sentence-level extractive summarization of news articles is the Lead-3 heuristic, where only the first 3 sentences are extracted. The success of this method is due to the tendency for writers to implement progressive elaboration in their work by writing the most important content at the beginning. In this paper, we introduce the Lead-like Recognizer (LeadR) to show how the Lead heuristic can be extended to summarize multi-section documents where it would not usually work well. This is done by introducing a neural model which produces a probability distribution over positions for sentences, so that we can locate sentences with introduction-like qualities. To evaluate the performance of our model, we use the task of summarizing multi-section documents. LeadR outperforms several baselines on this task, including a simple extension of the Lead heuristic designed for the task. Our work suggests that predicted position is a strong feature to use when extracting summaries.
leaflet Leaflet is a modern open-source JavaScript library for mobile-friendly interactive maps. It is developed by Vladimir Agafonkin with a team of dedicated contributors. Weighing just about 33 KB of JS, it has all the features most developers ever need for online maps. Leaflet is designed with simplicity, performance and usability in mind. It works efficiently across all major desktop and mobile platforms out of the box, taking advantage of HTML5 and CSS3 on modern browsers while still being accessible on older ones. It can be extended with a huge amount of plugins, has a beautiful, easy to use and well-documented API and a simple, readable source code that is a joy to contribute to.
http://…-neo4j-spatial-and-leaflet-js-with-mapbox
Leaflet: Interactive web maps with R
leaflet
Lean Analytics Lean Analytics is about measuring the right thing, in the right way, to produce the change the business needs the most at that point in time. With that in mind, here’s some background on metrics that matter.
Learnable Graph Convolutional Layer
(LGCL)
Convolutional neural networks (CNNs) have achieved great success on grid-like data such as images, but face tremendous challenges in learning from more generic data such as graphs. In CNNs, the trainable local filters enable the automatic extraction of high-level features. The computation with filters requires a fixed number of ordered units in the receptive fields. However, the number of neighboring units is neither fixed nor are they ordered in generic graphs, thereby hindering the applications of convolutional operations. Here, we address these challenges by proposing the learnable graph convolutional layer (LGCL). LGCL automatically selects a fixed number of neighboring nodes for each feature based on value ranking in order to transform graph data into grid-like structures in 1-D format, thereby enabling the use of regular convolutional operations on generic graphs. To enable model training on large-scale graphs, we propose a sub-graph training method to reduce the excessive memory and computational resource requirements suffered by prior methods on graph convolutions. Our experimental results on node classification tasks in both transductive and inductive learning settings demonstrate that our methods can achieve consistently better performance on the Cora, Citeseer, Pubmed citation network, and protein-protein interaction network datasets. Our results also indicate that the proposed methods using sub-graph training strategy are more efficient as compared to prior approaches.
Learnable Histogram Statistical features, such as histogram, Bag-of-Words (BoW) and Fisher Vector, were commonly used with hand-crafted features in conventional classification methods, but attract less attention since the popularity of deep learning methods. In this paper, we propose a learnable histogram layer, which learns histogram features within deep neural networks in end-to-end training. Such a layer is able to back-propagate (BP) errors, learn optimal bin centers and bin widths, and be jointly optimized with other layers in deep networks during training. Two vision problems, semantic segmentation and object detection, are explored by integrating the learnable histogram layer into deep networks, which show that the proposed layer could be well generalized to different applications. In-depth investigations are conducted to provide insights on the newly introduced layer.
Learn-As-You-Go
(LAGO)
Analysis of ‘Learn-As-You-Go’ (LAGO) Studies
Learning Active Learning
(LAL)
In this paper, we suggest a novel data-driven approach to active learning: Learning Active Learning (LAL). The key idea behind LAL is to train a regressor that predicts the expected error reduction for a potential sample in a particular learning state. By treating the query selection procedure as a regression problem we are not restricted to dealing with existing AL heuristics; instead, we learn strategies based on experience from previous active learning experiments. We show that LAL can be learnt from a simple artificial 2D dataset and yields strategies that work well on real data from a wide range of domains. Moreover, if some domain-specific samples are available to bootstrap active learning, the LAL strategy can be tailored for a particular problem.
Learning Analytics
(LA)
Learning analytics is the measurement, collection, analysis and reporting of data about learners and their contexts, for purposes of understanding and optimising learning and the environments in which it occurs. A related field is educational data mining. For general audience introductions, see:
· The Educause Learning Initiative Briefing
· The Educause Review on Learning analytics
· And the UNESCO “Learning Analytics Policy Brief” (2012)
Learning Automata Based SVM
(LA-SVM)
As an indispensable defensive measure of network security, the intrusion detection is a process of monitoring the events occurring in a computer system or network and analyzing them for signs of possible incidents. It is a classifier to judge the event is normal or malicious. The information used for intrusion detection contains some redundant features which would increase the difficulty of training the classifier for intrusion detection and increase the time of making predictions. To simplify the training process and improve the efficiency of the classifier, it is necessary to remove these dispensable features. in this paper, we propose a novel LA-SVM scheme to automatically remove redundant features focusing on intrusion detection. This is the first application of learning automata for solving dimension reduction problems. The simulation results indicate that the LA-SVM scheme achieves a higher accuracy and is more efficient in making predictions compared with traditional SVM.
Learning by Association In many real-world scenarios, labeled data for a specific machine learning task is costly to obtain. Semi-supervised training methods make use of abundantly available unlabeled data and a smaller number of labeled examples. We propose a new framework for semi-supervised training of deep neural networks inspired by learning in humans. ‘Associations’ are made from embeddings of labeled samples to those of unlabeled ones and back. The optimization schedule encourages correct association cycles that end up at the same class from which the association was started and penalizes wrong associations ending at a different class. The implementation is easy to use and can be added to any existing end-to-end training setup. We demonstrate the capabilities of learning by association on several data sets and show that it can improve performance on classification tasks tremendously by making use of additionally available unlabeled data. In particular, for cases with few labeled data, our training scheme outperforms the current state of the art on SVHN.
Learning Classifier System
(LCS)
Learning classifier systems, or LCS, are a paradigm of rule-based machine learning methods that combine a discovery component (e.g. typically a genetic algorithm) with a learning component (performing either supervised learning, reinforcement learning, or unsupervised learning).[2] Learning classifier systems seek to identify a set of context-dependent rules that collectively store and apply knowledge in a piecewise manner in order to make predictions (e.g. behavior modeling,[3] classification,[4][5] data mining,[5][6][7] regression,[8] function approximation,[9] or game strategy). This approach allows complex solution spaces to be broken up into smaller, simpler parts. The founding concepts behind learning classifier systems came from attempts to model complex adaptive systems, using rule-based agents to form an artificial cognitive system (i.e. artificial intelligence).
Learning Curve Plots relating performance to experience are widely used in machine learning. Performance is the error rate or accuracy of the learning system, while experience may be the number of training examples used for learning or the number of iterations used in optimizing the system model parameters. The machine learning curve is useful for many purposes including comparing different algorithms, choosing model parameters during design, adjusting optimization to improve convergence, and determining the amount of data used for training.
learning from Subgraphs, Embeddings, and Attributes for Link prediction
(SEAL)
Traditional methods for link prediction can be categorized into three main types: graph structure feature-based, latent feature-based, and explicit feature-based. Graph structure feature methods leverage some handcrafted node proximity scores, e.g., common neighbors, to estimate the likelihood of links. Latent feature methods rely on factorizing networks’ matrix representations to learn an embedding for each node. Explicit feature methods train a machine learning model on two nodes’ explicit attributes. Each of the three types of methods has its unique merits. In this paper, we propose SEAL (learning from Subgraphs, Embeddings, and Attributes for Link prediction), a new framework for link prediction which combines the power of all the three types into a single graph neural network (GNN). GNN is a new type of neural network which directly accepts graphs as input and outputs their labels. In SEAL, the input to the GNN is a local subgraph around each target link. We prove theoretically that our local subgraphs also reserve a great deal of high-order graph structure features related to link existence. Another key feature is that our GNN can naturally incorporate latent features and explicit features. It is achieved by concatenating node embeddings (latent features) and node attributes (explicit features) in the node information matrix for each subgraph, thus combining the three types of features to enhance GNN learning. Through extensive experiments, SEAL shows unprecedentedly strong performance against a wide range of baseline methods, including various link prediction heuristics and network embedding methods.
Learning M-Way Tree
(LMW-Tree)
LMW-tree is a generic template library written in C++ that implements several algorithms that use the m-way nearest neighbor tree structure to store their data. See the related PhD thesis for more details on m-way nn trees. The algorithms and data structures are generic to support different data representations such as dense real valued and bit vectors, and sparse vectors. Additionally, it can index any object type that can form a prototype representation of a set of objects. The algorithms are primarily focussed on computationally efficient clustering. Clustering is an unsupervised machine learning process that finds interesting patterns in data. It places similar items into clusters and dissimilar items into different clusters. The data structures and algorithms can also be used for nearest neighbor search, supervised learning and other machine learning applications. The package includes EM-tree, K-tree, k-means, TSVQ, repeated k-means, clustering, random projections, random indexing, hashing, bit signatures. See the related PhD thesis for more details these algorithms and representations. LMW-tree is licensed under the BSD license.
Learning Solving Procedure It is expected that progress toward true artificial intelligence will be achieved through the emergence of a system that integrates representation learning and complex reasoning (LeCun et al. 2015). In response to this prediction, research has been conducted on implementing the symbolic reasoning of a von Neumann computer in an artificial neural network (Graves et al. 2016; Graves et al. 2014; Reed et al. 2015). However, these studies have many limitations in realizing neural-symbolic integration (Jaeger. 2016). Here, we present a new learning paradigm: a learning solving procedure (LSP) that learns the procedure for solving complex problems. This is not accomplished merely by learning input-output data, but by learning algorithms through a solving procedure that obtains the output as a sequence of tasks for a given input problem. The LSP neural network system not only learns simple problems of addition and multiplication, but also the algorithms of complicated problems, such as complex arithmetic expression, sorting, and Hanoi Tower. To realize this, the LSP neural network structure consists of a deep neural network and long short-term memory, which are recursively combined. Through experimentation, we demonstrate the efficiency and scalability of LSP and its validity as a mechanism of complex reasoning.
Learning Through Deterministic Assignment of Hidden Parameters
(LtDaHP)
Supervised learning frequently boils down to determining hidden and bright parameters in a parameterized hypothesis space based on finite input-output samples. The hidden parameters determine the attributions of hidden predictors or the nonlinear mechanism of an estimator, while the bright parameters characterize how hidden predictors are linearly combined or the linear mechanism. In traditional learning paradigm, hidden and bright parameters are not distinguished and trained simultaneously in one learning process. Such an one-stage learning (OSL) brings a benefit of theoretical analysis but suffers from the high computational burden. To overcome this difficulty, a two-stage learning (TSL) scheme, featured by learning through deterministic assignment of hidden parameters (LtDaHP) was proposed, which suggests to deterministically generate the hidden parameters by using minimal Riesz energy points on a sphere and equally spaced points in an interval. We theoretically show that with such deterministic assignment of hidden parameters, LtDaHP with a neural network realization almost shares the same generalization performance with that of OSL. We also present a series of simulations and application examples to support the outperformance of LtDaHP
Learning to Coordinate and Teach Reinforcement
(LeCTR)
We present a framework and algorithm for peer-to-peer teaching in cooperative multiagent reinforcement learning. Our algorithm, Learning to Coordinate and Teach Reinforcement (LeCTR), trains advising policies by using students’ learning progress as a teaching reward. Agents using LeCTR learn to assume the role of a teacher or student at the appropriate moments, exchanging action advice to accelerate the entire learning process. Our algorithm supports teaching heterogeneous teammates, advising under communication constraints, and learns both what and when to advise. LeCTR is demonstrated to outperform the final performance and rate of learning of prior teaching methods on multiple benchmark domains. To our knowledge, this is the first approach for learning to teach in a multiagent setting.
Learning to Multitask
(L2MT)
Multitask learning has shown promising performance in many applications and many multitask models have been proposed. In order to identify an effective multitask model for a given multitask problem, we propose a learning framework called learning to multitask (L2MT). To achieve the goal, L2MT exploits historical multitask experience which is organized as a training set consists of several tuples, each of which contains a multitask problem with multiple tasks, a multitask model, and the relative test error. Based on such training set, L2MT first uses a proposed layerwise graph neural network to learn task embeddings for all the tasks in a multitask problem and then learns an estimation function to estimate the relative test error based on task embeddings and the representation of the multitask model based on a unified formulation. Given a new multitask problem, the estimation function is used to identify a suitable multitask model. Experiments on benchmark datasets show the effectiveness of the proposed L2MT framework.
Learning to Recommend with Missing Modalities
(LRMM)
Multimodal learning has shown promising performance in content-based recommendation due to the auxiliary user and item information of multiple modalities such as text and images. However, the problem of incomplete and missing modality is rarely explored and most existing methods fail in learning a recommendation model with missing or corrupted modalities. In this paper, we propose LRMM, a novel framework that mitigates not only the problem of missing modalities but also more generally the cold-start problem of recommender systems. We propose modality dropout (m-drop) and a multimodal sequential autoencoder (m-auto) to learn multimodal representations for complementing and imputing missing modalities. Extensive experiments on real-world Amazon data show that LRMM achieves state-of-the-art performance on rating prediction tasks. More importantly, LRMM is more robust to previous methods in alleviating data-sparsity and the cold-start problem.
Learning to Teach Teaching plays a very important role in our society, by spreading human knowledge and educating our next generations. A good teacher will select appropriate teaching materials, impact suitable methodologies, and set up targeted examinations, according to the learning behaviors of the students. In the field of artificial intelligence, however, one has not fully explored the role of teaching, and pays most attention to machine \emph{learning}. In this paper, we argue that equal attention, if not more, should be paid to teaching, and furthermore, an optimization framework (instead of heuristics) should be used to obtain good teaching strategies. We call this approach `learning to teach’. In the approach, two intelligent agents interact with each other: a student model (which corresponds to the learner in traditional machine learning algorithms), and a teacher model (which determines the appropriate data, loss function, and hypothesis space to facilitate the training of the student model). The teacher model leverages the feedback from the student model to optimize its own teaching strategies by means of reinforcement learning, so as to achieve teacher-student co-evolution. To demonstrate the practical value of our proposed approach, we take the training of deep neural networks (DNN) as an example, and show that by using the learning to teach techniques, we are able to use much less training data and fewer iterations to achieve almost the same accuracy for different kinds of DNN models (e.g., multi-layer perceptron, convolutional neural networks and recurrent neural networks) under various machine learning tasks (e.g., image classification and text understanding).
Learning Under Privileged Information
(LUPI)
Conformal Prediction in Learning Under Privileged Information Paradigm with Applications in Drug Discovery
Learning Vector Quantization
(LVQ)
In computer science, learning vector quantization (LVQ), is a prototype-based supervised classification algorithm. LVQ is the supervised counterpart of vector quantization systems.
Learning with Counts
Learning with Opponent-Learning Awareness
(LOLA)
Multi-agent settings are quickly gathering importance in machine learning. Beyond a plethora of recent work on deep multi-agent reinforcement learning, hierarchical reinforcement learning, generative adversarial networks and decentralized optimization can all be seen as instances of this setting. However, the presence of multiple learning agents in these settings renders the training problem non-stationary and often leads to unstable training or undesired final results. We present Learning with Opponent-Learning Awareness (LOLA), a method that reasons about the anticipated learning of the other agents. The LOLA learning rule includes an additional term that accounts for the impact of the agent’s policy on the anticipated parameter update of the other agents. We show that the LOLA update rule can be efficiently calculated using an extension of the likelihood ratio policy gradient update, making the method suitable for model-free reinforcement learning. This method thus scales to large parameter and input spaces and nonlinear function approximators. Preliminary results show that the encounter of two LOLA agents leads to the emergence of tit-for-tat and therefore cooperation in the infinitely iterated prisoners’ dilemma, while independent learning does not. In this domain, LOLA also receives higher payouts compared to a naive learner, and is robust against exploitation by higher order gradient-based methods. Applied to infinitely repeated matching pennies, only LOLA agents converge to the Nash equilibrium. We also apply LOLA to a grid world task with an embedded social dilemma using deep recurrent policies. Again, by considering the learning of the other agent, LOLA agents learn to cooperate out of selfish interests.
Learning-Based Visual Saliency Fusion Method for HDR Content
(LVBS-HDR)
Saliency prediction for Standard Dynamic Range (SDR) videos has been well explored in the last decade. However, limited studies are available on High Dynamic Range (HDR) Visual Attention Models (VAMs). Considering that the characteristic of HDR content in terms of dynamic range and color gamut is quite different than those of SDR content, it is essential to identify the importance of different saliency attributes of HDR videos for designing a VAM and understand how to combine these features. To this end we propose a learning-based visual saliency fusion method for HDR content (LVBS-HDR) to combine various visual saliency features. In our approach various conspicuity maps are extracted from HDR data, and then for fusing conspicuity maps, a Random Forests algorithm is used to train a model based on the collected data from an eye-tracking experiment. Performance evaluations demonstrate the superiority of the proposed fusion method against other existing fusion methods.
Least Absolute Deviation
(LAD)
Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute value (LAV), least absolute residual (LAR), sum of absolute deviations, or the L1 norm condition, is a statistical optimality criterion and the statistical optimization technique that relies on it. Similar to the popular least squares technique, it attempts to find a function which closely approximates a set of data. In the simple case of a set of (x,y) data, the approximation function is a simple ‘trend line’ in two-dimensional Cartesian coordinates. The method minimizes the sum of absolute errors (SAE) (the sum of the absolute values of the vertical ‘residuals’ between points generated by the function and corresponding points in the data). The least absolute deviations estimate also arises as the maximum likelihood estimate if the errors have a Laplace distribution.
LadR
Least Absolute Deviations
(LAD)
Least absolute deviations (LAD), also known as Least Absolute Errors (LAE), Least Absolute Value (LAV), or Least Absolute Residual (LAR) or the L1 norm problem, is a statistical optimization technique similar to the popular least squares technique that attempts to find a function which closely approximates a set of data. In the simple case of a set of (x,y) data, the approximation function is a simple ‘trend line’ in two-dimensional Cartesian coordinates. The method minimizes the sum of absolute errors (SAE) (the sum of the absolute values of the vertical ‘residuals’ between points generated by the function and corresponding points in the data). The least absolute deviations estimate also arises as the maximum likelihood estimate if the errors have a Laplace distribution.
Least Absolute Deviations Estimator
(LADE)
This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute deviations estimator (LADE) for the model. Second, we develop the random weighting (RW) method to estimate its asymptotic covariance matrix, leading to the implementation of the Wald test. Third, we construct a portmanteau test for model checking, and use the RW method to obtain its critical values. As a special weighted LADE, the feasible adaptive LADE (ALADE) is proposed and proved to have the same efficiency as its infeasible counterpart. The importance of our entire methodology based on the feasible ALADE is illustrated by simulation results and the real data analysis on three U.S. economic data sets.
Least Absolute Shrinkage and Screening Operator
(LASSO)
Slide 31: ‘Tibshirani (1996):
LASSO = Least Absolute Shrinkage and Selection Operator
new translation:
LASSO = Least Absolute Shrinkage and Screening Operator’
Least Absolute Shrinkage and Selection Operator
(LASSO)
The Lasso is a shrinkage and selection method for linear regression. It minimizes the usual sum of squared errors, with a bound on the sum of the absolute values of the coefficients. It has connections to soft-thresholding of wavelet coefficients, forward stagewise regression, and boosting methods.
Least Square Projection
(LSP)
The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analysis of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations compute the coordinates of a set of projected points based on the coordinates of a reduced number of control points with defined geometry. We name the technique Least Square Projections (LSP).
Least Squares Deep Q-Network
(LS-DQN)
Deep reinforcement learning (DRL) methods such as the Deep Q-Network (DQN) have achieved state-of-the-art results in a variety of challenging, high-dimensional domains. This success is mainly attributed to the power of deep neural networks to learn rich domain representations for approximating the value function or policy. Batch reinforcement learning methods with linear representations, on the other hand, are more stable and require less hyper parameter tuning. Yet, substantial feature engineering is necessary to achieve good results. In this work we propose a hybrid approach — the Least Squares Deep Q-Network (LS-DQN), which combines rich feature representations learned by a DRL algorithm with the stability of a linear least squares method. We do this by periodically re-training the last hidden layer of a DRL network with a batch least squares update. Key to our approach is a Bayesian regularization term for the least squares update, which prevents over-fitting to the more recent data. We tested LS-DQN on five Atari games and demonstrate significant improvement over vanilla DQN and Double-DQN. We also investigated the reasons for the superior performance of our method. Interestingly, we found that the performance improvement can be attributed to the large batch size used by the LS method when optimizing the last layer.
Least Squares Metric Learning
(LSML)
Relational Constraints for Metric Learning on Relational Data
Least-Angle Regression
(LARS)
In statistics, least-angle regression (LARS) is a regression algorithm for high-dimensional data, developed by Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani. Suppose we expect a response variable to be determined by a linear combination of a subset of potential covariates. Then the LARS algorithm provides a means of producing an estimate of which variables to include, as well as their coefficients. Instead of giving a vector result, the LARS solution consists of a curve denoting the solution for each value of the L1 norm of the parameter vector. The algorithm is similar to forward stepwise regression, but instead of including variables at each step, the estimated parameters are increased in a direction equiangular to each one’s correlations with the residual.
Leave-One-Out In this paper, we introduce a powerful technique, Leave-One-Out, to the analysis of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entry-wise bounds on iterative stochastic procedures. We demonstrate the power of this approach in analyzing two of the most important algorithms for matrix completion: the non-convex approach based on Singular Value Projection (SVP), and the convex relaxation approach based on nuclear norm minimization (NNM). In particular, we prove for the first time that the original form of SVP, without re-sampling or sample splitting, converges linearly in the infinity norm. We further apply our leave-one-out approach to an iterative procedure that arises in the analysis of the dual solutions of NNM. Our results show that NNM recovers the true $ d $-by-$ d $ rank-$ r $ matrix with $\mathcal{O}(\mu^2 r^3d \log d )$ observed entries, which has optimal dependence on the dimension and is independent of the condition number of the matrix. To the best of our knowledge, this is the first sample complexity result for a tractable matrix completion algorithm that satisfies these two properties simultaneously.
Leave-One-Out Cross Validation
(LOOCV)
Leave-one-out cross-validation (LOOCV) is a particular case of leave-p-out cross-validation with p = 1.
loo
Leave-p-Out Cross Validation
(LpOCV)
As the name suggests, leave-p-out cross-validation (LpO CV) involves using p observations as the validation set and the remaining observations as the training set. This is repeated on all ways to cut the original sample on a validation set of p’ observations and a training set. LpO cross-validation requires to learn and validate times (where n is the number of observation in the original sample). So as soon as n is quite big it becomes impossible to calculate.
Lecture Hall Tableaux We introduce lecture hall tableaux, which are fillings of a skew Young diagram satisfying certain conditions. Lecture hall tableaux generalize both lecture hall partitions and anti-lecture hall compositions, and also contain reverse semistandard Young tableaux as a limit case. We show that the coefficients in the Schur expansion of multivariate little $q$-Jacobi polynomials are generating functions for lecture hall tableaux. Using a Selberg-type integral we show that moments of multivariate little $q$-Jacobi polynomials, which are equal to generating functions for lecture hall tableaux of a Young diagram, have a product formula. We also explore various combinatorial properties of lecture hall tableaux.
LeFlow Recent work has shown that Field-Programmable Gate Arrays (FPGAs) play an important role in the acceleration of Machine Learning applications. Initial specification of machine learning applications are often done using a high-level Python-oriented framework such as Tensorflow, followed by a manual translation to either C or RTL for synthesis using vendor tools. This manual translation step is time-consuming and requires expertise that limit the applicability of FPGAs in this important domain. In this paper, we present an open-source tool-flow that maps numerical computation models written in Tensorflow to synthesizable hardware. Unlike other tools, which are often constrained by a small number of inflexible templates, our flow uses Google’s XLA compiler which emits LLVM code directly from a Tensorflow specification. This LLVM code can then be used with a high-level synthesis tool to automatically generate hardware. We show that our flow allows users to generate Deep Neural Networks with very few lines of Python code.
LemmaTag We present LemmaTag, a featureless recurrent neural network architecture that jointly generates part-of-speech tags and lemmatizes sentences of languages with complex morphology, using bidirectional RNNs with character-level and word-level embeddings. We demonstrate that both tasks benefit from sharing the encoding part of the network and from using the tagger output as an input to the lemmatizer. We evaluate our model across several morphologically-rich languages, surpassing state-of-the-art accuracy in both part-of-speech tagging and lemmatization in Czech, German, and Arabic.
Lemmatization Lemmatisation (or lemmatization) in linguistics is the process of grouping together the different inflected forms of a word so they can be analysed as a single item. In computational linguistics, lemmatisation is the algorithmic process of determining the lemma for a given word. Since the process may involve complex tasks such as understanding context and determining the part of speech of a word in a sentence (requiring, for example, knowledge of the grammar of a language) it can be a hard task to implement a lemmatiser for a new language. In many languages, words appear in several inflected forms. For example, in English, the verb ‘to walk’ may appear as ‘walk’, ‘walked’, ‘walks’, ‘walking’. The base form, ‘walk’, that one might look up in a dictionary, is called the lemma for the word. The combination of the base form with the part of speech is often called the lexeme of the word. Lemmatisation is closely related to stemming. The difference is that a stemmer operates on a single word without knowledge of the context, and therefore cannot discriminate between words which have different meanings depending on part of speech. However, stemmers are typically easier to implement and run faster, and the reduced accuracy may not matter for some applications.
Lempel–Ziv–Oberhumer
(LZO)
Lempel-Ziv-Oberhumer (LZO) is a lossless data compression algorithm that is focused on decompression speed.
Lenstra Lenstra Lovasz
(LLL)
The Lenstra-Lenstra-Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and László Lovász in 1982.
Level of Measurement Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio. This framework of distinguishing levels of measurement originated in psychology and is widely criticized by scholars in other disciplines. Other classifications include those by Mosteller and Tukey, and by Chrisman.
Levenberg-Marquardt Algorithm
(LMA)
In mathematics and computing, the Levenberg-Marquardt algorithm (LMA), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least squares curve fitting. The LMA interpolates between the Gauss-Newton algorithm (GNA) and the method of gradient descent. The LMA is more robust than the GNA, which means that in many cases it finds a solution even if it starts very far off the final minimum. For well-behaved functions and reasonable starting parameters, the LMA tends to be a bit slower than the GNA. LMA can also be viewed as Gauss-Newton using a trust region approach. The LMA is a very popular curve-fitting algorithm used in many software applications for solving generic curve-fitting problems. However, as for many fitting algorithms, the LMA finds only a local minimum, which is not necessarily the global minimum.
onls
Levenshtein Distance In information theory and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences. Informally, the Levenshtein distance between two words is the minimum number of single-character edits (i.e. insertions, deletions or substitutions) required to change one word into the other. The phrase edit distance is often used to refer specifically to Levenshtein distance. It is named after Vladimir Levenshtein, who considered this distance in 1965. It is closely related to pairwise string alignments.
Lexical Dispersion Plot A Lexical Dispersion Plot shows the position of words in a given text. On the y axis there is the list of words to be looked at and on the x axis there is the position in the text. Therefore the highest value on the x axis is the lenght of the text.
qdap
Lexical Table
Lexis Surface Map
LexNLP LexNLP is an open source Python package focused on natural language processing and machine learning for legal and regulatory text. The package includes functionality to (i) segment documents, (ii) identify key text such as titles and section headings, (iii) extract over eighteen types of structured information like distances and dates, (iv) extract named entities such as companies and geopolitical entities, (v) transform text into features for model training, and (vi) build unsupervised and supervised models such as word embedding or tagging models. LexNLP includes pre-trained models based on thousands of unit tests drawn from real documents available from the SEC EDGAR database as well as various judicial and regulatory proceedings. LexNLP is designed for use in both academic research and industrial applications, and is distributed at https://…/lexpredict-lexnlp.
LexVec In this paper, we propose LexVec, a new method for generating distributed word representations that uses low-rank, weighted factorization of the Positive Point-wise Mutual Information matrix via stochastic gradient descent, employing a weighting scheme that assigns heavier penalties for errors on frequent co-occurrences while still accounting for negative co-occurrence. Evaluation on word similarity and analogy tasks shows that LexVec matches and often outperforms state-of-the-art methods on many of these tasks.
libDirectional In this paper, we present libDirectional, a MATLAB library for directional statistics and directional estimation. It supports a variety of commonly used distributions on the unit circle, such as the von Mises, wrapped normal, and wrapped Cauchy distributions. Furthermore, various distributions on higher-dimensional manifolds such as the unit hypersphere and the hypertorus are available. Based on these distributions, several recursive filtering algorithms in libDirectional allow estimation on these manifolds. The functionality is implemented in a clear, well-documented, and object-oriented structure that is both easy to use and easy to extend.
libFM Factorization machines (FM) are a generic approach that allows to mimic most factorization models by feature engineering. This way, factorization machines combine the generality of feature engineering with the superiority of factorization models in estimating interactions between categorical variables of large domain. libFM is a software implementation for factorization machines that features stochastic gradient descent (SGD) and alternating least squares (ALS) optimization as well as Bayesian inference using Markov Chain Monte Carlo (MCMC).
LibLinear LibLinear is a linear classifier for data with millions of instances and features. It supports
· L2-regularized classifiers L2-loss linear SVM,
· L1-loss linear SVM, and logistic regression (LR)
· L1-regularized classifiers (after version 1.4)
· L2-loss linear SVM and logistic regression (LR)
· L2-regularized support vector regression (after version 1.9)
· L2-loss linear SVR and L1-loss linear SVR.
Library for Online Learning
(LIBOL)
LIBOL is an open-source library for large-scale online learning, which consists of a large family of e cient and scalable state-of-the-art online learning algorithms for large-scale online classification tasks. We have offered easy-to-use command-line tools and examples for users and developers, and also have made comprehensive documents available for both beginners and advanced users. LIBOL is not only a machine learning toolbox, but also a comprehensive experimental platform for conducting online learning research.
http://…/LIBOL_manual.pdf.
http://libol.stevenhoi.org
LIDIOMS In this paper, we describe the LIDIOMS data set, a multilingual RDF representation of idioms currently containing five languages: English, German, Italian, Portuguese, and Russian. The data set is intended to support natural language processing applications by providing links between idioms across languages. The underlying data was crawled and integrated from various sources. To ensure the quality of the crawled data, all idioms were evaluated by at least two native speakers. Herein, we present the model devised for structuring the data. We also provide the details of linking LIDIOMS to well-known multilingual data sets such as BabelNet. The resulting data set complies with best practices according to Linguistic Linked Open Data Community.
Lie Group Machine Learning
(LML)
In this paper a new method for dimensionality reduction in machine learning is pr oposed and called as Lie group Machine Learning (LML). The theory framework of LML is given , including the conception of one-parameter subgroup, Lie algebra and LML; the geometric properties of LML; the generalization hypothesis axiom, the partition independence hypothesis axiom, the duality hypothesis axiom, the learning compatibility hypothesis axiom of LML and the classifiers’ design of LML. The theory framework of Lie group machine learning (LML).
Survey on Lie Group Machine Learning
Lifelong Learning
(LL)
This paper proposes a novel lifelong learning (LL) approach to sentiment classification. LL mimics the human continuous learning process, i.e., retaining the knowledge learned from past tasks and use it to help future learning. In this paper, we first discuss LL in general and then LL for sentiment classification in particular. The proposed LL approach adopts a Bayesian optimization framework based on stochastic gradient descent. Our experimental results show that the proposed method outperforms baseline methods significantly, which demonstrates that lifelong learning is a promising research direction.
LIFT Reinforcement learning approaches have long appealed to the data management community due to their ability to learn to control dynamic behavior from raw system performance. Recent successes in combining deep neural networks with reinforcement learning have sparked significant new interest in this domain. However, practical solutions remain elusive due to large training data requirements, algorithmic instability, and lack of standard tools. In this work, we introduce LIFT, an end-to-end software stack for applying deep reinforcement learning to data management tasks. While prior work has frequently explored applications in simulations, LIFT centers on utilizing human expertise to learn from demonstrations, thus lowering online training times. We further introduce TensorForce, a TensorFlow library for applied deep reinforcement learning exposing a unified declarative interface to common RL algorithms, thus providing a backend to LIFT. We demonstrate the utility of LIFT in two case studies in database compound indexing and resource management in stream processing. Results show LIFT controllers initialized from demonstrations can outperform human baselines and heuristics across latency metrics and space usage by up to 70%.
lift
Lift Chart The lift chart provides a visual summary of the usefulness of the information provided by one or more statistical models for predicting a binomial (categorical) outcome variable (dependent variable); for multinomial (multiple-category) outcome variables, lift charts can be computed for each category. Specifically, the chart summarizes the utility that we may expect by using the respective predictive models, as compared to using baseline information only. The lift chart is applicable to most statistical methods that compute predictions (predicted classifications) for binomial or multinomial responses.
Let us start with an example. A marketing agency is planning to send advertisements to selected households with the goal to boost sales of a product. The agency has a list of all households where each household is described by a set of attributes. Each advertisement sent costs a few pennies, but it is well paid off if the customer buys the product. Therefore an agency wants to minimize the number of advertisements sent, while at the same time maximize the number of sold products by reaching only the consumers that will actually buy the product. Therefore it develops a classifier that predicts the probability that a household is a potential customer. To fit this classifier and to express the dependency between the costs and the expected benefit the lift chart can be used. The number off all potential customers P is often unknown, therefore TPrate cannot be computed and the ROC curve cannot used, but the lift chart is useful in such settings. Also the TP is often hard to measure in practice; one might have just a few measurements from a sales analysis. Even in such cases lift chart can help the agency select the amount of most promising households to which an advertisement should be sent. Of course, lift charts are also useful for many other similar problems.
http://…/vuk.pdf
A lift chart, sometimes called a cumulative gains chart, or a banana chart, is a measure of model performance. It shows how responses, (i.e., to a direct mail solicitation, or a surgical treatment for instance) are changed by applying the model. This change ratio, which is hopefully, the increase in response rate, is called the ‘lift’. A lift chart indicates which subset of the dataset contains the greatest possible proportion of positive responses. The higher the lift curve is from the baseline, the better the performance of the model since the baseline represents the null model, which is no model at all. To explain a lift chart, suppose we had a two-class prediction where the outcomes were yes (a positive response) or no (a negative response). To create a lift chart, instances in the dataset are sorted in descending probability order according to the predicted probability of a positive response. When the data is plotted, we can see a graphical depiction of the various probabilities. While the example shown in Figure 10 plots the results of different datasets for a single model, a lift chart can also be used to plot the results of a single dataset for different models. Note that the best model is not the one with the highest lift when it is being built. It is the model that performs the best on unseen, future data.
http://…/dm_c_ov.pdf
http://…/lift_chart.html
gains
Lifted Neural Network We describe a novel family of models of multi- layer feedforward neural networks in which the activation functions are encoded via penalties in the training problem. Our approach is based on representing a non-decreasing activation function as the argmin of an appropriate convex optimization problem. The new framework allows for algorithms such as block-coordinate descent methods to be applied, in which each step is composed of a simple (no hidden layer) supervised learning problem that is parallelizable across data points and/or layers. Experiments indicate that the proposed models provide excellent initial guesses for weights for standard neural networks. In addition, the model provides avenues for interesting extensions, such as robustness against noisy inputs and optimizing over parameters in activation functions.
Lifting The great advances of learning-based approaches in image processing and computer vision are largely based on deeply nested networks that compose linear transfer functions with suitable non-linearities. Interestingly, the most frequently used non-linearities in imaging applications (variants of the rectified linear unit) are uncommon in low dimensional approximation problems. In this paper we propose a novel non-linear transfer function, called lifting, which is motivated from a related technique in convex optimization. A lifting layer increases the dimensionality of the input, naturally yields a linear spline when combined with a fully connected layer, and therefore closes the gap between low and high dimensional approximation problems. Moreover, applying the lifting operation to the loss layer of the network allows us to handle non-convex and flat (zero-gradient) cost functions. We analyze the proposed lifting theoretically, exemplify interesting properties in synthetic experiments and demonstrate its effectiveness in deep learning approaches to image classification and denoising.
Light Recurrent Neural Networks
(LightRNN)
Recurrent neural networks (RNNs) have achieved state-of-the-art performances in many natural language processing tasks, such as language modeling and machine translation. However, when the vocabulary is large, the RNN model will become very big (e.g., possibly beyond the memory capacity of a GPU device) and its training will become very inefficient. In this work, we propose a novel technique to tackle this challenge. The key idea is to use 2-Component (2C) shared embedding for word representations. We allocate every word in the vocabulary into a table, each row of which is associated with a vector, and each column associated with another vector. Depending on its position in the table, a word is jointly represented by two components: a row vector and a column vector. Since the words in the same row share the row vector and the words in the same column share the column vector, we only need $2 \sqrt{|V|}$ vectors to represent a vocabulary of $|V|$ unique words, which are far less than the $|V|$ vectors required by existing approaches. Based on the 2-Component shared embedding, we design a new RNN algorithm and evaluate it using the language modeling task on several benchmark datasets. The results show that our algorithm significantly reduces the model size and speeds up the training process, without sacrifice of accuracy (it achieves similar, if not better, perplexity as compared to state-of-the-art language models). Remarkably, on the One-Billion-Word benchmark Dataset, our algorithm achieves comparable perplexity to previous language models, whilst reducing the model size by a factor of 40-100, and speeding up the training process by a factor of 2. We name our proposed algorithm \emph{LightRNN} to reflect its very small model size and very high training speed.
LightFM Model
(LightFM)
I present a hybrid matrix factorisation model representing users and items as linear combinations of their content features’ latent factors. The model outperforms both collaborative and content-based models in cold-start or sparse interaction data scenarios (using both user and item metadata), and performs at least as well as a pure collaborative matrix factorisation model where interaction data is abundant. Additionally, feature embeddings produced by the model encode semantic information in a way reminiscent of word embedding approaches, making them useful for a range of related tasks such as tag recommendations.
Lightweight Convolutional Neural Network
(LCNN)
Edge computing efficiently extends the realm of information technology beyond the boundary defined by cloud computing paradigm. Performing computation near the source and destination, edge computing is promising to address the challenges in many delay sensitive applications, like real time surveillance. Leveraging the ubiquitously connected cameras and smart mobile devices, it enables video analytics at the edge. However, traditional human objects detection and tracking approaches are still computationally too expensive to edge devices. Aiming at intelligent surveillance as an edge network service, this work explored the feasibility of two popular human objects detection schemes, Harr Cascade and SVM, at the edge. Understanding the existing constraints of the algorithms, a lightweight Convolutional Neural Network (LCNN) is proposed using the depthwise separable convolution. The proposed LCNN considerably reduces the number of parameters without affecting the quality of the output, thus it is ideal for an edge device usage. Being trained with Single Shot Multi box Detector (SSD) to pinpoint each human object location, it gives coordination of bounding box around the object. We implemented and tested LCNN on an edge device using Raspberry PI 3. The intensive experimental comparison study has validated that the proposed LCNN is a feasible design for real time human object detection as an edge service.
Lightweight Probabilistic Deep Network Even though probabilistic treatments of neural networks have a long history, they have not found widespread use in practice. Sampling approaches are often too slow already for simple networks. The size of the inputs and the depth of typical CNN architectures in computer vision only compound this problem. Uncertainty in neural networks has thus been largely ignored in practice, despite the fact that it may provide important information about the reliability of predictions and the inner workings of the network. In this paper, we introduce two lightweight approaches to making supervised learning with probabilistic deep networks practical: First, we suggest probabilistic output layers for classification and regression that require only minimal changes to existing networks. Second, we employ assumed density filtering and show that activation uncertainties can be propagated in a practical fashion through the entire network, again with minor changes. Both probabilistic networks retain the predictive power of the deterministic counterpart, but yield uncertainties that correlate well with the empirical error induced by their predictions. Moreover, the robustness to adversarial examples is significantly increased.
Lightweight Pyramid of Networks
(LPNet)
Existing deep convolutional neural networks have found major success in image deraining, but at the expense of an enormous number of parameters. This limits their potential application, for example in mobile devices. In this paper, we propose a lightweight pyramid of networks (LPNet) for single image deraining. Instead of designing a complex network structures, we use domain-specific knowledge to simplify the learning process. Specifically, we find that by introducing the mature Gaussian-Laplacian image pyramid decomposition technology to the neural network, the learning problem at each pyramid level is greatly simplified and can be handled by a relatively shallow network with few parameters. We adopt recursive and residual network structures to build the proposed LPNet, which has less than 8K parameters while still achieving state-of-the-art performance on rain removal. We also discuss the potential value of LPNet for other low- and high-level vision tasks.
Likelihood Likelihood is a funny concept. It’s not a probability, but it is proportional to a probability. The likelihood of a hypothesis (H) given some data (D) is proportional to the probability of obtaining D given that H is true, multiplied by an arbitrary positive constant (K). In other words, L(H|D) = K · P(D|H). Since a likelihood isn’t actually a probability it doesn’t obey various rules of probability. For example, likelihood need not sum to 1. A critical difference between probability and likelihood is in the interpretation of what is fixed and what can vary. In the case of a conditional probability, P(D|H), the hypothesis is fixed and the data are free to vary. Likelihood, however, is the opposite. The likelihood of a hypothesis, L(H|D), conditions on the data as if they are fixed while allowing the hypotheses to vary. The distinction is subtle, so I’ll say it again. For conditional probability, the hypothesis is treated as a given and the data are free to vary. For likelihood, the data are a given and the hypotheses vary.

http://…/likelihood

Likelihood Function In statistics, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model. The likelihood of a set of parameter values, theta, given outcomes x, is equal to the probability of those observed outcomes given those parameter values, that is L(theta|x) = P(x|theta).
Likelihood functions play a key role in statistical inference, especially methods of estimating a parameter from a set of statistics. In informal contexts, “likelihood” is often used as a synonym for “probability.” But in statistical usage, a distinction is made depending on the roles of the outcome or parameter. Probability is used when describing a function of the outcome given a fixed parameter value. For example, if a coin is flipped 10 times and it is a fair coin, what is the probability of it landing heads-up every time? Likelihood is used when describing a function of a parameter given an outcome. For example, if a coin is flipped 10 times and it has landed heads-up 10 times, what is the likelihood that the coin is fair?
Likelihood Ratio Similarity
(LiRa)
Recommender system data presents unique challenges to the data mining, machine learning, and algorithms communities. The high missing data rate, in combination with the large scale and high dimensionality that is typical of recommender systems data, requires new tools and methods for efficient data analysis. Here, we address the challenge of evaluating similarity between two users in a recommender system, where for each user only a small set of ratings is available. We present a new similarity score, that we call LiRa, based on a statistical model of user similarity, for large-scale, discrete valued data with many missing values. We show that this score, based on a ratio of likelihoods, is more effective at identifying similar users than traditional similarity scores in user-based collaborative filtering, such as the Pearson correlation coefficient. We argue that our approach has significant potential to improve both accuracy and scalability in collaborative filtering.
Likelihood-Ratio Test
(LRT)
In statistics, a likelihood ratio test is a statistical test used to compare the fit of two models, one of which (the null model) is a special case of the other (the alternative model). The test is based on the likelihood ratio, which expresses how many times more likely the data are under one model than the other. This likelihood ratio, or equivalently its logarithm, can then be used to compute a p-value, or compared to a critical value to decide whether to reject the null model in favour of the alternative model. When the logarithm of the likelihood ratio is used, the statistic is known as a log-likelihood ratio statistic, and the probability distribution of this test statistic, assuming that the null model is true, can be approximated using Wilks’s theorem. In the case of distinguishing between two models, each of which has no unknown parameters, use of the likelihood ratio test can be justified by the Neyman-Pearson lemma, which demonstrates that such a test has the highest power among all competitors.
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Likert Scale A Likert scale is a psychometric scale commonly involved in research that employs questionnaires. It is the most widely used approach to scaling responses in survey research, such that the term is often used interchangeably with rating scale, or more accurately the Likert-type scale, even though the two are not synonymous. The scale is named after its inventor, psychologist Rensis Likert. Likert distinguished between a scale proper, which emerges from collective responses to a set of items (usually eight or more), and the format in which responses are scored along a range. Technically speaking, a Likert scale refers only to the former.
likert,Scale
LIME-SUP Supervised Machine Learning (SML) algorithms such as Gradient Boosting, Random Forest, and Neural Networks have become popular in recent years due to their increased predictive performance over traditional statistical methods. This is especially true with large data sets (millions or more observations and hundreds to thousands of predictors). However, the complexity of the SML models makes them opaque and hard to interpret without additional tools. There has been a lot of interest recently in developing global and local diagnostics for interpreting and explaining SML models. In this paper, we propose locally interpretable models and effects based on supervised partitioning (trees) referred to as LIME-SUP. This is in contrast with the KLIME approach that is based on clustering the predictor space. We describe LIME-SUP based on fitting trees to the fitted response (LIM-SUP-R) as well as the derivatives of the fitted response (LIME-SUP-D). We compare the results with KLIME and describe its advantages using simulation and real data.
Limit Deterministic Buchi Automaton
(LDBA)
Logically-Correct Reinforcement Learning
Limited Memory Steepest Descent Method
(LMSD)
The possibilities inherent in steepest descent methods have been considerably amplified by the introduction of the Barzilai-Borwein choice of step-size, and other related ideas. These methods have proved to be competitive with conjugate gradient methods for the minimization of large dimension unconstrained minimization problems. This paper suggests a method which is able to take advantage of the availability of a few additional ‘long’ vectors of storage to achieve a significant improvement in performance, both for quadratic and non-quadratic objective functions. It makes use of certain Ritz values related to the Lanczos process (Lanczos in J Res Nat Bur Stand 45:255-282, 1950). Some underlying theory is provided, and numerical evidence is set out showing that the new method provides a competitive and more simple alternative to the state of the art l-BFGS limited memory method.
Limited-memory BFGS
(L-BFGS)
Limited-memory BFGS (L-BFGS or LM-BFGS) is an optimization algorithm in the family of quasi-Newton methods that approximates the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm using a limited amount of computer memory. It is a popular algorithm for parameter estimation in machine learning.
Lindy Effect The Lindy effect is a theory of the life expectancy of non-perishable things that posits for a certain class of nonperishables, like a technology or an idea, every additional day may imply a longer (remaining) life expectancy: the mortality rate decreases with time. This contrasts with living creatures and mechanical things, which instead follow a bathtub curve, where every additional day in its life translates into a shorter additional life expectancy (though longer overall life expectancy, due to surviving this far): after childhood, the mortality rate increases with time.
Line Map linemap
Linear Additive Markov Process
(LAMP)
We introduce LAMP: the Linear Additive Markov Process. Transitions in LAMP may be influenced by states visited in the distant history of the process, but unlike higher-order Markov processes, LAMP retains an efficient parametrization. LAMP also allows the specific dependence on history to be learned efficiently from data. We characterize some theoretical properties of LAMP, including its steady-state and mixing time. We then give an algorithm based on alternating minimization to learn LAMP models from data. Finally, we perform a series of real-world experiments to show that LAMP is more powerful than first-order Markov processes, and even holds its own against deep sequential models (LSTMs) with a negligible increase in parameter complexity.
Linear Algebra Package
(LAPACK)
LAPACK (Linear Algebra Package) is a software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition.
Linear Analog Self-Assessment
(LASA)
ordinalCont
Linear Attention Recurrent Neural Network
(LARNN)
The Linear Attention Recurrent Neural Network (LARNN) is a recurrent attention module derived from the Long Short-Term Memory (LSTM) cell and ideas from the consciousness Recurrent Neural Network (RNN). Yes, it LARNNs. The LARNN uses attention on its past cell state values for a limited window size $k$. The formulas are also derived from the Batch Normalized LSTM (BN-LSTM) cell and the Transformer Network for its Multi-Head Attention Mechanism. The Multi-Head Attention Mechanism is used inside the cell such that it can query its own $k$ past values with the attention window. This has the effect of augmenting the rank of the tensor with the attention mechanism, such that the cell can perform complex queries to question its previous inner memories, which should augment the long short-term effect of the memory. With a clever trick, the LARNN cell with attention can be easily used inside a loop on the cell state, just like how any other Recurrent Neural Network (RNN) cell can be looped linearly through time series. This is due to the fact that its state, which is looped upon throughout time steps within time series, stores the inner states in a ‘first in, first out’ queue which contains the $k$ most recent states and on which it is easily possible to add static positional encoding when the queue is represented as a tensor. This neural architecture yields better results than the vanilla LSTM cells. It can obtain results of 91.92% for the test accuracy, compared to the previously attained 91.65% using vanilla LSTM cells. Note that this is not to compare to other research, where up to 93.35% is obtained, but costly using 18 LSTM cells rather than with 2 to 3 cells as analyzed here. Finally, an interesting discovery is made, such that adding activation within the multi-head attention mechanism’s linear layers can yield better results in the context researched hereto.
Linear Centralization Classifier
(LCC)
A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center of their own classes, while maximimizing the distance between class centers. We formulate the classifier as a quadratic program with quadratic constraints. We then simplify this formulation to a linear program that can be solved effectively using a linear programming solver (e.g., simplex-dual). We extend the formulation for LCC to enable the use of kernel functions for non-linear classification applications. We compare our method with two standard classification methods (support vector machine and linear discriminant analysis) and four state-of-the-art classification methods when they are applied to eight standard classification datasets. Our experimental results show that LCC is able to classify instances more accurately (based on the area under the receiver operating characteristic) in comparison to other tested methods on the chosen datasets. We also report the results for LCC with a particular kernel to solve for synthetic non-linear classification problems.
Linear Congruential Generator
(LCG)
A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generator algorithms. The theory behind them is relatively easy to understand, and they are easily implemented and fast, especially on computer hardware which can provide modulo arithmetic by storage-bit truncation.
Linear Dimension Reduction Methods:
1. Principal component analysis (PCA)
2. Canonical correlation analysis (CCA)
3. Linear discriminant analysis (LDA)
4. Non-negative matrix factorization (NMF)
5. Independent component analysis (ICA)
LDRTools
Linear Discriminant Analysis
(LDA)
Linear discriminant analysis (LDA) and the related Fisher’s linear discriminant are methods used in statistics, pattern recognition and machine learning to find a linear combination of features which characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.
Fisher’s Linear Discriminant Analysis
Linear Discriminant Generative Adversarial Networks
(LD-GAN)
We develop a novel method for training of GANs for unsupervised and class conditional generation of images, called Linear Discriminant GAN (LD-GAN). The discriminator of an LD-GAN is trained to maximize the linear separability between distributions of hidden representations of generated and targeted samples, while the generator is updated based on the decision hyper-planes computed by performing LDA over the hidden representations. LD-GAN provides a concrete metric of separation capacity for the discriminator, and we experimentally show that it is possible to stabilize the training of LD-GAN simply by calibrating the update frequencies between generators and discriminators in the unsupervised case, without employment of normalization methods and constraints on weights. In the class conditional generation tasks, the proposed method shows improved training stability together with better generalization performance compared to WGAN that employs an auxiliary classifier.
Linear k-Junta We study the problem of testing if a function depends on a small number of linear directions of its input data. We call a function $f$ a \emph{linear $k$-junta} if it is completely determined by some $k$-dimensional subspace of the input space. In this paper, we study the problem of testing whether a given $n$ variable function $f : \mathbb{R}^n \to $, is a linear $k$-junta or $\epsilon$-far from all linear $k$-juntas, where the closeness is measured with respect to the Gaussian measure on $\mathbb{R}^n$. This problems is a common generalization of (i) The combinatorial problem of junta testing on the hypercube which tests whether a Boolean function is dependent on at most $k$ of its variables and (ii) Geometric testing problems such as testing if a function is an intersection of $k$ halfspaces. We prove the existence of a $\mathsf{poly}(k \cdot s/\epsilon)$-query non-adaptive tester for linear $k$-juntas with surface area at most $s$. The polynomial dependence on $s$ is necessary as we provide a $\mathsf{poly}(s)$ lower bound on the query complexity of any non-adaptive test for linear juntas. Moreover, we show that if the function is a linear $k$-junta with surface area at most $s$, then there is a $(s \cdot k)^{O(k)}$-query non-adaptive algorithm to learn the function \emph{up to a rotation of the basis}. {We also use this procedure to obtain a non-adaptive tester (with the same query complexity) for subclasses of linear $k$-juntas closed under rotation.}
Linear Mixed Effects Model CLME,lmenssp
Linear Mixed Model
(LMM)
A statistical model containing both fixed effects and random effects, that is: mixed effects. LMM is a kind of regression analysis.
Linear Model U-Tree
(LMUT)
Deep Reinforcement Learning (DRL) has achieved impressive success in many applications. A key component of many DRL models is a neural network representing a Q function, to estimate the expected cumulative reward following a state-action pair. The Q function neural network contains a lot of implicit knowledge about the RL problems, but often remains unexamined and uninterpreted. To our knowledge, this work develops the first mimic learning framework for Q functions in DRL. We introduce Linear Model U-trees (LMUTs) to approximate neural network predictions. An LMUT is learned using a novel on-line algorithm that is well-suited for an active play setting, where the mimic learner observes an ongoing interaction between the neural net and the environment. Empirical evaluation shows that an LMUT mimics a Q function substantially better than five baseline methods. The transparent tree structure of an LMUT facilitates understanding the network’s learned knowledge by analyzing feature influence, extracting rules, and highlighting the super-pixels in image inputs.
Linear Programming
(LP)
Linear programming (LP; also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polyhedron, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine function defined on this polyhedron. A linear programming algorithm finds a point in the polyhedron where this function has the smallest (or largest) value if such a point exists.
Linear Quadratic Estimation
(LQE)
Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing noise (random variations) and other inaccuracies, and produces estimates of unknown variables that tend to be more precise than those based on a single measurement alone. More formally, the Kalman filter operates recursively on streams of noisy input data to produce a statistically optimal estimate of the underlying system state. The filter is named after Rudolf (Rudy) E. Kálmán, one of the primary developers of its theory. The Kalman filter has numerous applications in technology. A common application is for guidance, navigation and control of vehicles, particularly aircraft and spacecraft. Furthermore, the Kalman filter is a widely applied concept in time series analysis used in fields such as signal processing and econometrics. Kalman filters also are one of the main topics in the field of Robotic motion planning and control, and sometimes included in Trajectory optimization.
Linear Regression In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variable) denoted X. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression. (This term should be distinguished from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.)
In linear regression, data are modeled using linear predictor functions, and unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, linear regression refers to a model in which the conditional mean of y given the value of X is an affine function of X. Less commonly, linear regression could refer to a model in which the median, or some other quantile of the conditional distribution of y given X is expressed as a linear function of X. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of y given X, rather than on the joint probability distribution of y and X, which is the domain of multivariate analysis.
Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications. This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine.
Linear regression has many practical uses. Most applications fall into one of the following two broad categories:
· If the goal is prediction, or forecasting, or reduction, linear regression can be used to fit a predictive model to an observed data set of y and X values. After developing such a model, if an additional value of X is then given without its accompanying value of y, the fitted model can be used to make a prediction of the value of y.
· Given a variable y and a number of variables X1, …, Xp that may be related to y, linear regression analysis can be applied to quantify the strength of the relationship between y and the Xj, to assess which Xj may have no relationship with y at all, and to identify which subsets of the Xj contain redundant information about y.
Linear regression models are often fitted using the least squares approach, but they may also be fitted in other ways, such as by minimizing the ‘lack of fit’ in some other norm (as with least absolute deviations regression), or by minimizing a penalized version of the least squares loss function as in ridge regression (L2-norm penalty) and lasso (L1-norm penalty). Conversely, the least squares approach can be used to fit models that are not linear models. Thus, although the terms ‘least squares’ and ‘linear model’ are closely linked, they are not synonymous.
Linear Superiorization
(LinSup)
Linear superiorization (abbreviated: LinSup) considers linear programming (LP) problems wherein the constraints as well as the objective function are linear. It allows to steer the iterates of a feasibility-seeking iterative process toward feasible points that have lower (not necessarily minimal) values of the objective function than points that would have been reached by the same feasiblity-seeking iterative process without superiorization. Using a feasibility-seeking iterative process that converges even if the linear feasible set is empty, LinSup generates an iterative sequence that converges to a point that minimizes a proximity function which measures the linear constraints violation. In addition, due to LinSup’s repeated objective function reduction steps such a point will most probably have a reduced objective function value. We present an exploratory experimental result that illustrates the behavior of LinSup on an infeasible LP problem.
Linear Unified LASSO
(LLASSO)
We propose a rescaled LASSO, by premultipying the LASSO with a matrix term, namely linear unified LASSO (LLASSO) for multicollinear situations. Our numerical study has shown that the LLASSO is comparable with other sparse modeling techniques and often outperforms the LASSO and elastic net. Our findings open new visions about using the LASSO still for sparse modeling and variable selection. We conclude our study by pointing that the LLASSO can be solved by the same efficient algorithm for solving the LASSO and suggest to follow the same construction technique for other penalized estimators.
Linearized Binary Regression Probit regression was first proposed by Bliss in 1934 to study mortality rates of insects. Since then, an extensive body of work has analyzed and used probit or related binary regression methods (such as logistic regression) in numerous applications and fields. This paper provides a fresh angle to such well-established binary regression methods. Concretely, we demonstrate that linearizing the probit model in combination with linear estimators performs on par with state-of-the-art nonlinear regression methods, such as posterior mean or maximum aposteriori estimation, for a broad range of real-world regression problems. We derive exact, closed-form, and nonasymptotic expressions for the mean-squared error of our linearized estimators, which clearly separates them from nonlinear regression methods that are typically difficult to analyze. We showcase the efficacy of our methods and results for a number of synthetic and real-world datasets, which demonstrates that linearized binary regression finds potential use in a variety of inference, estimation, signal processing, and machine learning applications that deal with binary-valued observations or measurements.
Linear-Time Clustering Algorithm
(K-sets+)
In this paper, we first propose a new iterative algorithm, called the K-sets+ algorithm for clustering data points in a semi-metric space, where the distance measure does not necessarily satisfy the triangular inequality. We show that the K-sets+ algorithm converges in a finite number of iterations and it retains the same performance guarantee as the K-sets algorithm for clustering data points in a metric space. We then extend the applicability of the K-sets+ algorithm from data points in a semi-metric space to data points that only have a symmetric similarity measure. Such an extension leads to great reduction of computational complexity. In particular, for an n * n similarity matrix with m nonzero elements in the matrix, the computational complexity of the K-sets+ algorithm is O((Kn + m)I), where I is the number of iterations. The memory complexity to achieve that computational complexity is O(Kn + m). As such, both the computational complexity and the memory complexity are linear in n when the n * n similarity matrix is sparse, i.e., m = O(n). We also conduct various experiments to show the effectiveness of the K-sets+ algorithm by using a synthetic dataset from the stochastic block model and a real network from the WonderNetwork website.
Linear-Time Detection of Non-Linear Changes
(LIGHT)
Change detection in multivariate time series has applications in many domains, including health care and network monitoring. A common approach to detect changes is to compare the divergence between the distributions of a reference window and a test window. When the number of dimensions is very large, however, the na¨ıve approach has both quality and efficiency issues: to ensure robustness the window size needs to be large, which not only leads to missed alarms but also increases runtime. To this end, we propose LIGHT, a linear-time algorithm for robustly detecting non-linear changes in massively high dimensional time series. Importantly, LIGHT provides high flexibility in choosing the window size, allowing the domain expert to fit the level of details required. To do such, we 1) perform scalable PCA to reduce dimensionality, 2) perform scalable factorization of the joint distribution, and 3) scalably compute divergences between these lower dimensional distributions. Extensive empirical evaluation on both synthetic and real-world data show that LIGHT outperforms state of the art with up to 100% improvement in both quality and efficiency.
LineNet High Definition (HD) maps play an important role in modern traffic scenes. However, the development of HD maps coverage grows slowly because of the cost limitation. To efficiently model HD maps, we proposed a convolutional neural network with a novel prediction layer and a zoom module, called LineNet. It is designed for state-of-the-art lane detection in an unordered crowdsourced image dataset. And we introduced TTLane, a dataset for efficient lane detection in urban road modeling applications. Combining LineNet and TTLane, we proposed a pipeline to model HD maps with crowdsourced data for the first time. And the maps can be constructed precisely even with inaccurate crowdsourced data.
Linguistic Descriptions of Complex Phenomena
(LDCP)
Linguistic Descriptions of Complex Phenomena (LDCP) is an architecture and methodology that allows us to model complex phenomena, interpreting input data, and generating automatic text reports customized to the user needs (see <doi:10.1016/j.ins.2016.11.002> and <doi:10.1007/s00500-016-2430-5> ).
rLDCP
Link Function In GLM, the link function provides the relationship between the linear predictor and the mean of the distribution function. There are many commonly used link functions, and their choice can be somewhat arbitrary. It makes sense to try to match the domain of the link function to the range of the distribution function’s mean.
Link Prediction Given a snapshot of a social network, can we infer which new interactions among its members are likely to occur in the near future? We formalize this question as the link prediction problem, and develop approaches to link prediction based on measures for analyzing the \proximity” of nodes in a network. Experiments on large co-authorship networks suggest that information about future interactions can be extracted from network topology alone, and that fairly subtle measures for detecting node proximity can outperform more direct measures.
Linked Causal Variational Autoencoder
(LCVA)
Modeling spillover effects from observational data is an important problem in economics, business, and other fields of research. % It helps us infer the causality between two seemingly unrelated set of events. For example, if consumer spending in the United States declines, it has spillover effects on economies that depend on the U.S. as their largest export market. In this paper, we aim to infer the causation that results in spillover effects between pairs of entities (or units), we call this effect as \textit{paired spillover}. To achieve this, we leverage the recent developments in variational inference and deep learning techniques to propose a generative model called Linked Causal Variational Autoencoder (LCVA). Similar to variational autoencoders (VAE), LCVA incorporates an encoder neural network to learn the latent attributes and a decoder network to reconstruct the inputs. However, unlike VAE, LCVA treats the \textit{latent attributes as confounders that are assumed to affect both the treatment and the outcome of units}. Specifically, given a pair of units $u$ and $\bar{u}$, their individual treatment and outcomes, the encoder network of LCVA samples the confounders by conditioning on the observed covariates of $u$, the treatments of both $u$ and $\bar{u}$ and the outcome of $u$. Once inferred, the latent attributes (or confounders) of $u$ captures the spillover effect of $\bar{u}$ on $u$. Using a network of users from job training dataset (LaLonde (1986)) and co-purchase dataset from Amazon e-commerce domain, we show that LCVA is significantly more robust than existing methods in capturing spillover effects.
Linked Data Ranking Algorithm
(LDRANK)
The advances of the Linked Open Data (LOD) initiative are giving rise to a more structured Web of data. Indeed, a few datasets act as hubs (e.g., DBpedia) connecting many other datasets. They also made possible new Web services for entity detection inside plain text (e.g., DBpedia Spotlight), thus allowing for new applications that can benefit from a combination of the Web of documents and the Web of data. To ease the emergence of these new applications, we propose a query-biased algorithm (LDRANK) for the ranking of web of data resources with associated textual data. Our algorithm combines link analysis with dimensionality reduction. We use crowdsourcing for building a publicly available and reusable dataset for the evaluation of query-biased ranking of Web of data resources detected in Web pages. We show that, on this dataset, LDRANK outperforms the state of the art. Finally, we use this algorithm for the construction of semantic snippets of which we evaluate the usefulness with a crowdsourcing-based approach.
Linked Matrix Factorization
(LMF)
In recent years, a number of methods have been developed for the dimension reduction and decomposition of multiple linked high-content data matrices. Typically these methods assume that just one dimension, rows or columns, is shared among the data sources. This shared dimension may represent common features that are measured for different sample sets (i.e., horizontal integration) or a common set of samples with measurements for different feature sets (i.e., vertical integration). In this article we introduce an approach for simultaneous horizontal and vertical integration, termed Linked Matrix Factorization (LMF), for the more general situation where some matrices share rows (e.g., features) and some share columns (e.g., samples). Our motivating application is a cytotoxicity study with accompanying genomic and molecular chemical attribute data. In this data set, the toxicity matrix (cell lines $\times$ chemicals) shares its sample set with a genotype matrix (cell lines $\times$ SNPs), and shares its feature set with a chemical molecular attribute matrix (chemicals $\times$ attributes). LMF gives a unified low-rank factorization of these three matrices, which allows for the decomposition of systematic variation that is shared among the three matrices and systematic variation that is specific to each matrix. This may be used for efficient dimension reduction, exploratory visualization, and the imputation of missing data even when entire rows or columns are missing from a constituent data matrix. We present theoretical results concerning the uniqueness, identifiability, and minimal parametrization of LMF, and evaluate it with extensive simulation studies.
Linked Micromaps Linked Micromaps is a graphing program written in Java. It allows users to view multiple variables interactively and compare statistics across regions (states, counties, registries, hospitals) as well as across time. It supports six types of graph:
· bar graphs;
· box plots;
· raw data tables;
· point graphs;
· point graphs with arrow; and
· point graphs with confidence intervals.
Linked Recurrent Neural Network
(LinkedRNN)
Recurrent Neural Networks (RNNs) have been proven to be effective in modeling sequential data and they have been applied to boost a variety of tasks such as document classification, speech recognition and machine translation. Most of existing RNN models have been designed for sequences assumed to be identically and independently distributed (i.i.d). However, in many real-world applications, sequences are naturally linked. For example, web documents are connected by hyperlinks; and genes interact with each other. On the one hand, linked sequences are inherently not i.i.d., which poses tremendous challenges to existing RNN models. On the other hand, linked sequences offer link information in addition to the sequential information, which enables unprecedented opportunities to build advanced RNN models. In this paper, we study the problem of RNN for linked sequences. In particular, we introduce a principled approach to capture link information and propose a linked Recurrent Neural Network (LinkedRNN), which models sequential and link information coherently. We conduct experiments on real-world datasets from multiple domains and the experimental results validate the effectiveness of the proposed framework.
Links We present a novel algorithm, called Links, designed to perform online clustering on unit vectors in a high-dimensional Euclidean space. The algorithm is appropriate when it is necessary to cluster data efficiently as it streams in, and is to be contrasted with traditional batch clustering algorithms that have access to all data at once. For example, Links has been successfully applied to embedding vectors generated from face images or voice recordings for the purpose of recognizing people, thereby providing real-time identification during video or audio capture.
Liquid Analytics Liquid analytics. That’s the part that automatically updates and refines the training sets, rules, inferences, confidence intervals and predictions, every day, as mutating data keeps pouring non-stop in the databases (be it NoSQL or not). While this (most of the time) still ends up being coded in production mode by software engineers or developers, the framework and logical architecture is designed by data scientists. Because of this, data science is to data floods what statistical science is to frozen data.
LISAL Most environmental phenomena, such as wind profiles, ozone concentration and sunlight distribution under a forest canopy, exhibit nonstationary dynamics i.e. phenomenon variation change depending on the location and time of occurrence. Non-stationary dynamics pose both theoretical and practical challenges to statistical machine learning algorithms aiming to accurately capture the complexities governing the evolution of such processes. In this paper, we address the sampling aspects of the problem of learning nonstationary spatio-temporal models, and propose an efficient yet simple algorithm – LISAL. The core idea in LISAL is to learn two models using Gaussian processes (GPs) wherein the first is a nonstationary GP directly modeling the phenomenon. The second model uses a stationary GP representing a latent space corresponding to changes in dynamics, or the nonstationarity characteristics of the first model. LISAL involves adaptively sampling the latent space dynamics using information theory quantities to reduce the computational cost during the learning phase. The relevance of LISAL is extensively validated using multiple real world datasets.
Efficiently Learning Nonstationary Gaussian Processes
ListOps Latent tree learning models learn to parse a sentence without syntactic supervision, and use that parse to build the sentence representation. Existing work on such models has shown that, while they perform well on tasks like sentence classification, they do not learn grammars that conform to any plausible semantic or syntactic formalism (Williams et al., 2018a). Studying the parsing ability of such models in natural language can be challenging due to the inherent complexities of natural language, like having several valid parses for a single sentence. In this paper we introduce ListOps, a toy dataset created to study the parsing ability of latent tree models. ListOps sequences are in the style of prefix arithmetic. The dataset is designed to have a single correct parsing strategy that a system needs to learn to succeed at the task. We show that the current leading latent tree models are unable to learn to parse and succeed at ListOps. These models achieve accuracies worse than purely sequential RNNs.
LISTwise ExplaiNer
(LISTEN)
There is an increasing demand for algorithms to explain their outcomes. So far, there is no method that explains the rankings produced by a ranking algorithm. To address this gap we propose LISTEN, a LISTwise ExplaiNer, to explain rankings produced by a ranking algorithm. To efficiently use LISTEN in production, we train a neural network to learn the underlying explanation space created by LISTEN; we call this model Q-LISTEN. We show that LISTEN produces faithful explanations and that Q-LISTEN is able to learn these explanations. Moreover, we show that LISTEN is safe to use in a real world environment: users of a news recommendation system do not behave significantly differently when they are exposed to explanations generated by LISTEN instead of manually generated explanations.
Literate Programming Literate programming is an approach to programming introduced by Donald Knuth in which a program is given as an explanation of the program logic in a natural language, such as English, interspersed with snippets of macros and traditional source code, from which a compilable source code can be generated.
littler (“little R”) littler provides the r program, a simplified command-line interface for GNU R. This allows direct execution of commands, use in piping where the output of one program supplies the input of the next, as well as adding the ability for writing hash-bang scripts, i.e. creating executable files starting with, say, #!/usr/bin/r.
GNU R, a language and environment for statistical computing and graphics, provides a wonderful system for ‘programming with data’ as well as interactive exploratory analysis, often involving graphs. Sometimes, however, simple scripts are desired. While R can be used in batch mode, and while so-called here documents can be crafted, a long-standing need for a scripting front-end has often been expressed by the R Community. littler (pronounced little R and written r) aims to fill this need.
Ljung-Box Test The Ljung-Box test (named for Greta M. Ljung and George E. P. Box) is a type of statistical test of whether any of a group of autocorrelations of a time series are different from zero. Instead of testing randomness at each distinct lag, it tests the ‘overall’ randomness based on a number of lags, and is therefore a portmanteau test. This test is sometimes known as the Ljung-Box Q test, and it is closely connected to the Box-Pierce test (which is named after George E. P. Box and David A. Pierce). In fact, the Ljung-Box test statistic was described explicitly in the paper that led to the use of the Box-Pierce statistic, and from which that statistic takes its name. The Box-Pierce test statistic is a simplified version of the Ljung-Box statistic for which subsequent simulation studies have shown poor performance. The Ljung-Box test is widely applied in econometrics and other applications of time series analysis.
http://…/ljung-box-test
Lloyd-Max In computer science and electrical engineering, Lloyd’s algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced sets of points in subsets of Euclidean spaces, and partitions of these subsets into well-shaped and uniformly sized convex cells. Like the closely related k-means clustering algorithm, it repeatedly finds the centroid of each set in the partition, and then re-partitions the input according to which of these centroids is closest. However, Lloyd’s algorithm differs from k-means clustering in that its input is a continuous geometric region rather than a discrete set of points. Thus, when re-partitioning the input, Lloyd’s algorithm uses Voronoi diagrams rather than simply determining the nearest center to each of a finite set of points as the k-means algorithm does. Although the algorithm may be applied most directly to the Euclidean plane, similar algorithms may also be applied to higher-dimensional spaces or to spaces with other non-Euclidean metrics. Lloyd’s algorithm can be used to construct close approximations to centroidal Voronoi tessellations of the input, which can be used for quantization, dithering, and stippling. Other applications of Lloyd’s algorithm include smoothing of triangle meshes in the finite element method.
“Compressive K-means”
LMKL-Net In this paper we propose solving localized multiple kernel learning (LMKL) using LMKL-Net, a feedforward deep neural network. In contrast to previous works, as a learning principle we propose {\em parameterizing} both the gating function for learning kernel combination weights and the multiclass classifier in LMKL using an attentional network (AN) and a multilayer perceptron (MLP), respectively. In this way we can learn the (nonlinear) decision function in LMKL (approximately) by sequential applications of AN and MLP. Empirically on benchmark datasets we demonstrate that overall LMKL-Net can not only outperform the state-of-the-art MKL solvers in terms of accuracy, but also be trained about {\em two orders of magnitude} faster with much smaller memory footprint for large-scale learning.
Local Average Treatment Effect
(LATE)
Local Binary Convolution
(LBC)
We propose local binary convolution (LBC), an efficient alternative to convolutional layers in standard convolutional neural networks (CNN). The design principles of LBC are motivated by local binary patterns (LBP). The LBC layer comprises of a set of fixed sparse pre-defined binary convolutional filters that are not updated during the training process, a non-linear activation function and a set of learnable linear weights. The linear weights combine the activated filter responses to approximate the corresponding activated filter responses of a standard convolutional layer. The LBC layer affords significant parameter savings, 9x to 169x in the number of learnable parameters compared to a standard convolutional layer. Furthermore, due to lower model complexity and sparse and binary nature of the weights also results in up to 9x to 169x savings in model size compared to a standard convolutional layer. We demonstrate both theoretically and experimentally that our local binary convolution layer is a good approximation of a standard convolutional layer. Empirically, CNNs with LBC layers, called local binary convolutional neural networks (LBCNN), reach state-of-the-art performance on a range of visual datasets (MNIST, SVHN, CIFAR-10, and a subset of ImageNet) while enjoying significant computational savings.
Local Binary Pattern Network
(LBPNet)
Memory and computation efficient deep learning architec- tures are crucial to continued proliferation of machine learning capabili- ties to new platforms and systems. Binarization of operations in convo- lutional neural networks has shown promising results in reducing model size and computing efficiency. In this paper, we tackle the problem us- ing a strategy different from the existing literature by proposing local binary pattern networks or LBPNet, that is able to learn and perform binary operations in an end-to-end fashion. LBPNet1 uses local binary comparisons and random projection in place of conventional convolu- tion (or approximation of convolution) operations. These operations can be implemented efficiently on different platforms including direct hard- ware implementation. We applied LBPNet and its variants on standard benchmarks. The results are promising across benchmarks while provid- ing an important means to improve memory and speed efficiency that is particularly suited for small footprint devices and hardware accelerators.
Local Coordinate Coding
(LCC)
Generative adversarial networks (GANs) aim to generate realistic data from some prior distribution (e.g., Gaussian noises). However, such prior distribution is often independent of real data and thus may lose semantic information (e.g., geometric structure or content in images) of data. In practice, the semantic information might be represented by some latent distribution learned from data, which, however, is hard to be used for sampling in GANs. In this paper, rather than sampling from the pre-defined prior distribution, we propose a Local Coordinate Coding (LCC) based sampling method to improve GANs. We derive a generalization bound for LCC based GANs and prove that a small dimensional input is sufficient to achieve good generalization. Extensive experiments on various real-world datasets demonstrate the effectiveness of the proposed method.
Local Differential Privacy Real-time data-driven optimization and control problems over networks may require sensitive information of participating users to calculate solutions and decision variables, such as in traffic or energy systems. Adversaries with access to coordination signals may potentially decode information on individual users and put user privacy at risk. We develop \emph{local differential privacy}, which is a strong notion that guarantees user privacy regardless of any auxiliary information an adversary may have, for a larger family of convex distributed optimization problems. The mechanism allows agent to customize their own privacy level based on local needs and parameter sensitivities. We propose a general sampling based approach for determining sensitivity and derive analytical bounds for specific quadratic problems. We analyze inherent trade-offs between privacy and suboptimality and propose allocation schemes to divide the maximum allowable noise, a \emph{privacy budget}, among all participating agents. Our algorithm is implemented to enable privacy in distributed optimal power flow for electric grids.
Local Error Driven and Associative Biologically Realistic Algorithm
(leabra)
The algorithm Leabra (local error driven and associative biologically realistic algorithm) allows for the construction of artificial neural networks that are biologically realistic and balance supervised and unsupervised learning within a single framework.
leabRa
Local Expansion via Minimum One Norm
(LEMON)
We propose a novel approach for finding overlapping communities called LEMON (Local Expansion via Minimum One Norm). The algorithm finds the community by seeking a sparse vector in the span of the local spectra such that the seeds are in its support. We show that LEMON can achieve the highest detection accuracy among state-of-the-art proposals. The running time depends on the size of the community rather than that of the entire graph. The algorithm is easy to implement, and is highly parallelizable.
Local False Discovery Rate
(LFDR)
“False Discovery Rate”
LFDR.MLE
Local Fisher Discriminant Analysis
(LFDA)
lfda
Local Gradients Smoothing
(LGS)
Deep neural networks (DNNs) have shown vulnerability to adversarial attacks, i.e., carefully perturbed inputs designed to mislead the network at inference time. Recently introduced localized attacks, LaVAN and Adversarial patch, posed a new challenge to deep learning security by adding adversarial noise only within a specific region without affecting the salient objects in an image. Driven by the observation that such attacks introduce concentrated high-frequency changes at a particular image location, we have developed an effective method to estimate noise location in gradient domain and transform those high activation regions caused by adversarial noise in image domain while having minimal effect on the salient object that is important for correct classification. Our proposed Local Gradients Smoothing (LGS) scheme achieves this by regularizing gradients in the estimated noisy region before feeding the image to DNN for inference. We have shown the effectiveness of our method in comparison to other defense methods including JPEG compression, Total Variance Minimization (TVM) and Feature squeezing on ImageNet dataset. In addition, we systematically study the robustness of the proposed defense mechanism against Back Pass Differentiable Approximation (BPDA), a state of the art attack recently developed to break defenses that transform an input sample to minimize the adversarial effect. Compared to other defense mechanisms, LGS is by far the most resistant to BPDA in localized adversarial attack setting.
LOcal Group Graphical Lasso Estimation
(loggle)
In this paper, we study time-varying graphical models based on data measured over a temporal grid. Such models are motivated by the needs to describe and understand evolving interacting relationships among a set of random variables in many real applications, for instance the study of how stocks interact with each other and how such interactions change over time. We propose a new model, LOcal Group Graphical Lasso Estimation (loggle), under the assumption that the graph topology changes gradually over time. Specifically, loggle uses a novel local group-lasso type penalty to efficiently incorporate information from neighboring time points and to impose structural smoothness of the graphs. We implement an ADMM based algorithm to fit the loggle model. This algorithm utilizes blockwise fast computation and pseudo-likelihood approximation to improve computational efficiency. An R package loggle has also been developed. We evaluate the performance of loggle by simulation experiments. We also apply loggle to S&P 500 stock price data and demonstrate that loggle is able to reveal the interacting relationships among stocks and among industrial sectors in a time period that covers the recent global financial crisis.
Local Interpretable Model-Agnostic Explanation
(LIME)
Machine learning is at the core of many recent advances in science and technology. With computers beating professionals in games like Go, many people have started asking if machines would also make for better drivers or even better doctors. In many applications of machine learning, users are asked to trust a model to help them make decisions. A doctor will certainly not operate on a patient simply because ‘the model said so.’ Even in lower-stakes situations, such as when choosing a movie to watch from Netflix, a certain measure of trust is required before we surrender hours of our time based on a model. Despite the fact that many machine learning models are black boxes, understanding the rationale behind the model’s predictions would certainly help users decide when to trust or not to trust their predictions. An example is shown in Figure 1, in which a model predicts that a certain patient has the flu. The prediction is then explained by an ‘explainer’ that highlights the symptoms that are most important to the model. With this information about the rationale behind the model, the doctor is now empowered to trust the model-or not.
Local Linear Forest Random forests are a powerful method for non-parametric regression, but are limited in their ability to fit smooth signals, and can show poor predictive performance in the presence of strong, smooth effects. Taking the perspective of random forests as an adaptive kernel method, we pair the forest kernel with a local linear regression adjustment to better capture smoothness. The resulting procedure, local linear forests, enables us to improve on asymptotic rates of convergence for random forests with smooth signals, and provides substantial gains in accuracy on both real and simulated data.
Local Mahalanobis Distance Learning
(LMDL)
Distance metric learning is a successful way to enhance the performance of the nearest neighbor classifier. In most cases, however, the distribution of data does not obey a regular form and may change in different parts of the feature space. Regarding that, this paper proposes a novel local distance metric learning method, namely Local Mahalanobis Distance Learning (LMDL), in order to enhance the performance of the nearest neighbor classifier. LMDL considers the neighborhood influence and learns multiple distance metrics for a reduced set of input samples. The reduced set is called as prototypes which try to preserve local discriminative information as much as possible. The proposed LMDL can be kernelized very easily, which is significantly desirable in the case of highly nonlinear data. The quality as well as the efficiency of the proposed method assesses through a set of different experiments on various datasets and the obtained results show that LDML as well as the kernelized version is superior to the other related state-of-the-art methods.
Local Outlier Factor
(LOF)
In anomaly detection, the local outlier factor (LOF) is an algorithm proposed by Markus M. Breunig, Hans-Peter Kriegel, Raymond T. Ng and Jörg Sander in 2000 for finding anomalous data points by measuring the local deviation of a given data point with respect to its neighbours. LOF shares some concepts with DBSCAN and OPTICS such as the concepts of ‘core distance’ and ‘reachability distance’, which are used for local density estimation.
Rlof
Local Projections In this paper, we propose a novel approach for outlier detection, called local projections, which is based on concepts of Local Outlier Factor (LOF) (Breunig et al., 2000) and RobPCA (Hubert et al., 2005). By using aspects of both methods, our algorithm is robust towards noise variables and is capable of performing outlier detection in multi-group situations. We are further not reliant on a specific underlying data distribution. For each observation of a dataset, we identify a local group of dense nearby observations, which we call a core, based on a modification of the k-nearest neighbours algorithm. By projecting the dataset onto the space spanned by those observations, two aspects are revealed. First, we can analyze the distance from an observation to the center of the core within the projection space in order to provide a measure of quality of description of the observation by the projection. Second, we consider the distance of the observation to the projection space in order to assess the suitability of the core for describing the outlyingness of the observation. These novel interpretations lead to a univariate measure of outlyingness based on aggregations over all local projections, which outperforms LOF and RobPCA as well as other popular methods like PCOut (Filzmoser et al., 2008) and subspace-based outlier detection (Kriegel et al., 2009) in our simulation setups. Experiments in the context of real-word applications employing datasets of various dimensionality demonstrate the advantages of local projections.
Local Regression
(LOESS, LOWESS)
LOESS and LOWESS (locally weighted scatterplot smoothing) are two strongly related non-parametric regression methods that combine multiple regression models in a k-nearest-neighbor-based meta-model. “LOESS” is a later generalization of LOWESS; although it is not a true initialism, it may be understood as standing for “LOcal regrESSion”.
Local Reparameterization Network
(LR-Nets)
Recent breakthroughs in computer vision make use of large deep neural networks, utilizing the substantial speedup offered by GPUs. For applications running on limited hardware however, high precision real-time processing can still be a challenge. One approach to solve this problem is learning networks with binary or ternary weights, thus removing the need to calculate multiplications and significantly reduce memory size and access. In this work we introduce LR-nets (Local reparameterization networks), a new method for training neural networks with discrete weights using stochastic parameters. We show how a simple modification to the local reparameterization trick, previously used to train Gaussian distributed weights, allows us to train discrete weights. We tested our method on MNIST, CIFAR-10 and ImageNet, achieving state-of-the-art results compared to previous binary and ternary models.
Local Shrunk Discriminant Analysis
(LSDA)
Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which is often employed to seek a projection to best represent the data in a least-squares sense, but if the original data is nonlinear structure, the performance of PCA will quickly drop. An supervised dimensionality reduction algorithm called Linear discriminant analysis (LDA) seeks for an embedding transformation, which can work well with Gaussian distribution data or single-modal data, but for non-Gaussian distribution data or multimodal data, it gives undesired results. What is worse, the dimension of LDA cannot be more than the number of classes. In order to solve these issues, Local shrunk discriminant analysis (LSDA) is proposed in this work to process the non-Gaussian distribution data or multimodal data, which not only incorporate both the linear and nonlinear structures of original data, but also learn the pattern shrinking to make the data more flexible to fit the manifold structure. Further, LSDA has more strong generalization performance, whose objective function will become local LDA and traditional LDA when different extreme parameters are utilized respectively. What is more, a new efficient optimization algorithm is introduced to solve the non-convex objective function with low computational cost. Compared with other related approaches, such as PCA, LDA and local LDA, the proposed method can derive a subspace which is more suitable for non-Gaussian distribution and real data. Promising experimental results on different kinds of data sets demonstrate the effectiveness of the proposed approach.
Locality Sensitive Hashing
(LSH)
Locality-sensitive hashing (LSH) is a method of performing probabilistic dimension reduction of high-dimensional data. The basic idea is to hash the input items so that similar items are mapped to the same buckets with high probability (the number of buckets being much smaller than the universe of possible input items). This is different from the conventional hash functions, such as those used in cryptography, as in the LSH case the goal is to maximize probability of ‘collision’ of similar items rather than avoid collisions. Note how locality-sensitive hashing, in many ways, mirrors data clustering and Nearest neighbor search.
http://…/LSH
http://…description-of-locality-sensitive-hashing
Localization Recall Precision
(LRP)
Average precision (AP), the area under the recall-precision (RP) curve, is the standard performance measure for object detection. Despite its wide acceptance, it has a number of shortcomings, the most important of which are (i) the inability to distinguish very different RP curves, and (ii) the lack of directly measuring bounding box localization accuracy. In this paper, we propose ‘Localization Recall Precision (LRP) Error’, a new metric which we specifically designed for object detection. LRP Error is composed of three components related to localization, false negative (FN) rate and false positive (FP) rate. Based on LRP, we introduce the ‘Optimal LRP’, the minimum achievable LRP error representing the best achievable configuration of the detector in terms of recall-precision and the tightness of the boxes. In contrast to AP, which considers precisions over the entire recall domain, Optimal LRP determines the ‘best’ confidence score threshold for a class, which balances the trade-off between localization and recall-precision. In our experiments, we show that, for state-of-the-art object (SOTA) detectors, Optimal LRP provides richer and more discriminative information than AP. We also demonstrate that the best confidence score thresholds vary significantly among classes and detectors. Moreover, we present LRP results of a simple online video object detector which uses a SOTA still image object detector and show that the class-specific optimized thresholds increase the accuracy against the common approach of using a general threshold for all classes. We provide the source code that can compute LRP for the PASCAL VOC and MSCOCO datasets in https://…/LRP. Our source code can easily be adapted to other datasets as well.
Localized Information Privacy
(LIP)
In this paper, localized information privacy (LIP) is proposed, as a new privacy definition, which allows statistical aggregation while protecting users’ privacy without relying on a trusted third party. The notion of context-awareness is incorporated in LIP by the introduction of priors, which enables the design of privacy-preserving data aggregation with knowledge of priors. We show that LIP relaxes the Localized Differential Privacy (LDP) notion by explicitly modeling the adversary’s knowledge. However, it is stricter than $2\epsilon$-LDP and $\epsilon$-mutual information privacy. The incorporation of local priors allows LIP to achieve higher utility compared to other approaches. We then present an optimization framework for privacy-preserving data aggregation, with the goal of minimizing the expected squared error while satisfying the LIP privacy constraints. Utility-privacy tradeoffs are obtained under several models in closed-form. We then validate our analysis by {numerical analysis} using both synthetic and real-world data. Results show that our LIP mechanism provides better utility-privacy tradeoffs than LDP and when the prior is not uniformly distributed, the advantage of LIP is even more significant.
Locally Estimated Scatterplot Smoothing
(LOESS)
LOESS and LOWESS (locally weighted scatterplot smoothing) are two strongly related non-parametric regression methods that combine multiple regression models in a k-nearest-neighbor-based meta-model. “LOESS” is a later generalization of LOWESS; although it is not a true initialism, it may be understood as standing for “LOcal regrESSion”.
Locally Linear Embedding
(LLE)
Locally Linear Embedding (LLE), an unsupervised learning algorithm that computes low dimensional, neighborhood preserving embeddings of high dimensional data. LLE attempts to discover nonlinear structure in high dimensional data by exploiting the local symmetries of linear reconstructions. Notably, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations – though capable of generating highly nonlinear embeddings – do not involve local minima.
http://…/2323.full.pdf
Locally Smoothed Neural Network
(LSNN)
Convolutional Neural Networks (CNN) and the locally connected layer are limited in capturing the importance and relations of different local receptive fields, which are often crucial for tasks such as face verification, visual question answering, and word sequence prediction. To tackle the issue, we propose a novel locally smoothed neural network (LSNN) in this paper. The main idea is to represent the weight matrix of the locally connected layer as the product of the kernel and the smoother, where the kernel is shared over different local receptive fields, and the smoother is for determining the importance and relations of different local receptive fields. Specifically, a multi-variate Gaussian function is utilized to generate the smoother, for modeling the location relations among different local receptive fields. Furthermore, the content information can also be leveraged by setting the mean and precision of the Gaussian function according to the content. Experiments on some variant of MNIST clearly show our advantages over CNN and locally connected layer.
Locate-Link-Visualize
(LocLinkVis)
In this paper we present LocLinkVis (Locate-Link-Visualize); a system which supports exploratory information access to a document collection based on geo-referencing and visualization. It uses a gazetteer which contains representations of places ranging from countries to buildings, and that is used to recognize toponyms, disambiguate them into places, and to visualize the resulting spatial footprints.
Location Determination Problem
(LDP)
Log Gaussian Cox Process Network We generalize the log Gaussian Cox process (LGCP) framework to model multiple correlated point data jointly. The resulting log Gaussian Cox process network (LGCPN) considers the observations as realizations of multiple LGCPs, whose log intensities are given by linear combinations of latent functions drawn from Gaussian process priors. The coefficients of these linear combinations are also drawn from Gaussian processes and can incorporate additional dependencies a priori. We derive closed-form expressions for the moments of the intensity functions in our model and use them to develop an efficient variational inference algorithm that is orders of magnitude faster than competing deterministic and stochastic approximations of multivariate LGCP and coregionalization models. Our approach outperforms the state of the art in jointly estimating multiple bovine tuberculosis incidents in Cornwall, UK, and multiple crime type intensities across New York city.
LogCanvas In this demo paper, we introduce LogCanvas, a platform for user search history visualisation. Different from the existing visualisation tools, LogCanvas focuses on helping users re-construct the semantic relationship among their search activities. LogCanvas segments a user’s search history into different sessions and generates a knowledge graph to represent the information exploration process in each session. A knowledge graph is composed of the most important concepts or entities discovered by each search query as well as their relationships. It thus captures the semantic relationship among the queries. LogCanvas offers a session timeline viewer and a snippets viewer to enable users to re-find their previous search results efficiently. LogCanvas also provides a collaborative perspective to support a group of users in sharing search results and experience.
Logic Learning Machine
(LLM)
Logic Learning Machine (LLM) is a machine learning method based on the generation of intelligible rules. LLM is an efficient implementation of the Switching Neural Network (SNN) paradigm, developed by Marco Muselli, Senior Researcher at the Italian National Research Council CNR-IEIIT in Genoa. Logic Learning Machine is implemented in the Rulex suite. LLM has been employed in different fields, including orthopaedic patient classification, DNA microarray analysis and Clinical Decision Support System.
Logically-Correct Reinforcement Learning We propose a novel Reinforcement Learning (RL) algorithm to synthesize policies for a Markov Decision Process (MDP), such that a linear time property is satisfied. We convert the property into a Limit Deterministic Buchi Automaton (LDBA), then construct a product MDP between the automaton and the original MDP. A reward function is then assigned to the states of the product automaton, according to accepting conditions of the LDBA. With this reward function, RL synthesizes a policy that satisfies the property: as such, the policy synthesis procedure is ‘constrained’ by the given specification. Additionally, we show that the RL procedure sets up an online value iteration method to calculate the maximum probability of satisfying the given property, at any given state of the MDP – a convergence proof for the procedure is provided. Finally, the performance of the algorithm is evaluated via a set of numerical examples. We observe an improvement of one order of magnitude in the number of iterations required for the synthesis compared to existing approaches.
Logistic Regression In statistics, logistic regression, or logit regression, is a type of probabilistic statistical classification model. It is also used to predict a binary response from a binary predictor, used for predicting the outcome of a categorical dependent variable (i.e., a class label) based on one or more predictor variables (features). That is, it is used in estimating empirical values of the parameters in a qualitative response model. The probabilities describing the possible outcomes of a single trial are modeled, as a function of the explanatory (predictor) variables, using a logistic function. Frequently (and subsequently in this article) “logistic regression” is used to refer specifically to the problem in which the dependent variable is binary-that is, the number of available categories is two-while problems with more than two categories are referred to as multinomial logistic regression or, if the multiple categories are ordered, as ordered logistic regression.
logit The logit function is the inverse of the sigmoidal “logistic” function used in mathematics, especially in statistics. When the function’s parameter represents a probability p, the logit function gives the log-odds, or the logarithm of the odds p/(1-p).
LogitBoost Autoregressive Networks Multivariate binary distributions can be decomposed into products of univariate conditional distributions. Recently popular approaches have modeled these conditionals through neural networks with sophisticated weight-sharing structures. It is shown that state-of-the-art performance on several standard benchmark datasets can actually be achieved by training separate probability estimators for each dimension. In that case, model training can be trivially parallelized over data dimensions. On the other hand, complexity control has to be performed for each learned conditional distribution. Three possible methods are considered and experimentally compared. The estimator that is employed for each conditional is LogitBoost. Similarities and differences between the proposed approach and autoregressive models based on neural networks are discussed in detail.
Log-Likelihood For many applications, the natural logarithm of the likelihood function, called the log-likelihood, is more convenient to work with. Because the logarithm is a monotonically increasing function, the logarithm of a function achieves its maximum value at the same points as the function itself, and hence the log-likelihood can be used in place of the likelihood in maximum likelihood estimation and related techniques. Finding the maximum of a function often involves taking the derivative of a function and solving for the parameter being maximized, and this is often easier when the function being maximized is a log-likelihood rather than the original likelihood function. For example, some likelihood functions are for the parameters that explain a collection of statistically independent observations. In such a situation, the likelihood function factors into a product of individual likelihood functions. The logarithm of this product is a sum of individual logarithms, and the derivative of a sum of terms is often easier to compute than the derivative of a product. In addition, several common distributions have likelihood functions that contain products of factors involving exponentiation. The logarithm of such a function is a sum of products, again easier to differentiate than the original function. In phylogenetics the log-likelihood ratio is sometimes termed support and the log-likelihood function support function. However, given the potential for confusion with the mathematical meaning of ‘support’ this terminology is rarely used outside this field.
Log-Linear Model A log-linear model is a mathematical model that takes the form of a function whose logarithm is a first-degree polynomial function of the parameters of the model, which makes it possible to apply (possibly multivariate) linear regression.
Log-rank Test In statistics, the log-rank test is a hypothesis test to compare the survival distributions of two samples. It is a nonparametric test and appropriate to use when the data are right skewed and censored (technically, the censoring must be non-informative). It is widely used in clinical trials to establish the efficacy of a new treatment in comparison with a control treatment when the measurement is the time to event (such as the time from initial treatment to a heart attack). The test is sometimes called the Mantel-Cox test, named after Nathan Mantel and David Cox. The log-rank test can also be viewed as a time-stratified Cochran-Mantel-Haenszel test.
glrt
LoIDE Logic-based paradigms are nowadays widely used in many different fields, also thank to the availability of robust tools and systems that allow the development of real-world and industrial applications. In this work we present LoIDE, an advanced and modular web-editor for logic-based languages that also integrates with state-of-the-art solvers.
LOKI Imitation learning (IL) consists of a set of tools that leverage expert demonstrations to quickly learn policies. However, if the expert is suboptimal, IL can yield policies with inferior performance compared to reinforcement learning (RL). In this paper, we aim to provide an algorithm that combines the best aspects of RL and IL. We accomplish this by formulating several popular RL and IL algorithms in a common mirror descent framework, showing that these algorithms can be viewed as a variation on a single approach. We then propose LOKI, a strategy for policy learning that first performs a small but random number of IL iterations before switching to a policy gradient RL method. We show that if the switching time is properly randomized, LOKI can learn to outperform a suboptimal expert and converge faster than running policy gradient from scratch. Finally, we evaluate the performance of LOKI experimentally in several simulated environments.
Long- and Short-Term Time-Series Network
(LSTNet)
Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these real-world applications often involves a mixture of long-term and short-term patterns, for which traditional approaches such as Autoregressive models and Gaussian Process may fail. In this paper, we proposed a novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge. LSTNet uses the Convolution Neural Network (CNN) to extract short-term local dependency patterns among variables, and the Recurrent Neural Network (RNN) to discover long-term patterns and trends. In our evaluation on real-world data with complex mixtures of repetitive patterns, LSTNet achieved significant performance improvements over that of several state-of-the-art baseline methods.
Long Short Term Memory
(LSTM)
Long short term memory (LSTM) is a recurrent neural network (RNN) architecture (an artificial neural network) published in 1997 by Sepp Hochreiter and Jürgen Schmidhuber. Like most RNNs, an LSTM network is universal in the sense that given enough network units it can compute anything a conventional computer can compute, provided it has the proper weight matrix, which may be viewed as its program. (Of course, finding such a weight matrix is more challenging with some problems than with others.) Unlike traditional RNNs, an LSTM network is well-suited to learn from experience to classify, process and predict time series when there are very long time lags of unknown size between important events. This is one of the main reasons why LSTM outperforms alternative RNNs and Hidden Markov Models and other sequence learning methods in numerous applications. For example, LSTM achieved the best known results in unsegmented connected handwriting recognition, and in 2009 won the ICDAR handwriting competition. LSTM networks have also been used for automatic speech recognition, and were a major component of a network that recently achieved a record 17.7% phoneme error rate on the classic TIMIT natural speech dataset.
Longitudinal Study A longitudinal survey is a correlational research study that involves repeated observations of the same variables over long periods of time – often many decades. It is a type of observational study. Longitudinal studies are often used in psychology to study developmental trends across the life span, and in sociology to study life events throughout lifetimes or generations. The reason for this is that, unlike cross-sectional studies, in which different individuals with same characteristics are compared, longitudinal studies track the same people, and therefore the differences observed in those people are less likely to be the result of cultural differences across generations. Because of this benefit, longitudinal studies make observing changes more accurate, and they are applied in various other fields. In medicine, the design is used to uncover predictors of certain diseases. In advertising, the design is used to identify the changes that advertising has produced in the attitudes and behaviors of those within the target audience who have seen the advertising campaign. Because most longitudinal studies are observational, in the sense that they observe the state of the world without manipulating it, it has been argued that they may have less power to detect causal relationships than experiments. But because of the repeated observation at the individual level, they have more power than cross-sectional observational studies, by virtue of being able to exclude time-invariant unobserved individual differences, and by virtue of observing the temporal order of events. Some of the disadvantages of longitudinal study include the fact that they take a lot of time and are very expensive. Therefore, they are not very convenient. Longitudinal studies allow social scientists to distinguish short from long-term phenomena, such as poverty. If the poverty rate is 10% at a point in time, this may mean that 10% of the population are always poor, or that the whole population experiences poverty for 10% of the time. It is impossible to conclude which of these possibilities is the case using one-off cross-sectional studies. Types of longitudinal studies include cohort studies and panel studies. Cohort studies sample a cohort, defined as a group experiencing some event (typically birth) in a selected time period, and studying them at intervals through time. Panel studies sample a cross-section, and survey it at (usually regular) intervals. A retrospective study is a longitudinal study that looks back in time. For instance, a researcher may look up the medical records of previous years to look for a trend.
Long-Range Dependency
(LRD)
Long-range dependency (LRD), also called long memory or long-range persistence, is a phenomenon that may arise in the analysis of spatial or time series data. It relates to the rate of decay of statistical dependence, with the implication that this decays more slowly than an exponential decay, typically a power-like decay. LRD is often related to self-similar processes or fields. LRD has been used in various fields such as internet traffic modelling, econometrics, hydrology, linguistics and the earth sciences. Different mathematical definitions of LRD are used for different contexts and purposes.
Lookup-Based Convolutional Neural Network
(LCNN)
Porting state of the art deep learning algorithms to resource constrained compute platforms (e.g. VR, AR, wearables) is extremely challenging. We propose a fast, compact, and accurate model for convolutional neural networks that enables efficient learning and inference. We introduce LCNN, a lookup-based convolutional neural network that encodes convolutions by few lookups to a dictionary that is trained to cover the space of weights in CNNs. Training LCNN involves jointly learning a dictionary and a small set of linear combinations. The size of the dictionary naturally traces a spectrum of trade-offs between efficiency and accuracy. Our experimental results on ImageNet challenge show that LCNN can offer 3.2x speedup while achieving 55.1% top-1 accuracy using AlexNet architecture. Our fastest LCNN offers 37.6x speed up over AlexNet while maintaining 44.3% top-1 accuracy. LCNN not only offers dramatic speed ups at inference, but it also enables efficient training. In this paper, we show the benefits of LCNN in few-shot learning and few-iteration learning, two crucial aspects of on-device training of deep learning models.
Lord’s Paradox In statistics, Lord’s paradox raises the issue of when it is appropriate to control for baseline status. In three papers, Frederic Lord noted that different results obtain if researchers adjust for pre-existing differences. The paradox was resolved by Paul Holland and Donald Rubin using the Rubin causal model. The most famous formulation of Lord’s paradox was in his 1967 paper and was phrased in terms of weight change over freshman year of college in two different dormitories because Lord did not want readers to assume that measurement error was responsible for the paradox. ‘A large university is interested in investigating the effects on the students of the diet provided in the university dining halls and any sex differences in these effects. Various types of data are gathered. In particular, the weight of each student at the time of his arrival in September and his weight the following June are recorded.’ (Lord 1967, p. 304)
Resolving the Lord’s Paradox
Lorenz Curve In economics, the Lorenz curve is a graphical representation of the cumulative distribution function of the empirical probability distribution of wealth or income, and was developed by Max O. Lorenz in 1905 for representing inequality of the wealth distribution. The curve is a graph showing the proportion of overall income or wealth assumed by the bottom x% of the people, although this is not rigorously true for a finite population (see below). It is often used to represent income distribution, where it shows for the bottom x% of households, what percentage (y%) of the total income they have. The percentage of households is plotted on the x-axis, the percentage of income on the y-axis. It can also be used to show distribution of assets. In such use, many economists consider it to be a measure of social inequality. The concept is useful in describing inequality among the size of individuals in ecology and in studies of biodiversity, where the cumulative proportion of species is plotted against the cumulative proportion of individuals. It is also useful in business modeling: e.g., in consumer finance, to measure the actual percentage y% of delinquencies attributable to the x% of people with worst risk scores.
Loss Data Analytics Loss Data Analytics is an interactive, online, freely available text. The idea behind the name Loss Data Analytics is to integrate classical loss data models from applied probability with modern analytic tools. In particular, we seek to recognize that big data (including social media and usage based insurance) are here and high speed computation is readily available. The online version contains many interactive objects (quizzes, computer demonstrations, interactive graphs, video, and the like) to promote deeper learning. A subset of the book is available for offline reading in pdf and EPUB formats. The online text will be available in multiple languages to promote access to a worldwide audience.
Loss Distributional Approach
(LDA)
While AMA does not specify the use of any particular modeling technique, one common approach taken in the banking industry is the Loss Distribution Approach (LDA). With LDA, a bank first segments operational losses into homogeneous segments, called unit of measure’s (UoMs). For each unit of measure, the bank then constructs a loss distribution that represents its expectation of total losses that can materialize in a one-year horizon. Given that data sufficiency is a major challenge for the industry, annual loss distribution cannot be built directly using annual loss figures. Instead, a bank will develop a frequency distribution that describes the number of loss events in a given year, and a severity distribution that describes the loss amount of a single loss event. The frequency and severity distributions are assumed to be independent. The convolution of these two distributions then give rise to the (annual) loss distribution.
Loss Function In mathematical optimization, statistics, decision theory and machine learning, a loss function or cost function is a function that maps an event or values of one or more variables onto a real number intuitively representing some ‘cost’ associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its negative (sometimes called a reward function or a utility function), in which case it is to be maximized. In statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced in statistics by Abraham Wald in the middle of the 20th Century. In the context of economics, for example, this is usually economic cost or regret. In classification, it is the penalty for an incorrect classification of an example. In actuarial science, it is used in an insurance context to model benefits paid over premiums, particularly since the works of Harald Cramér in the 1920s. In optimal control the loss is the penalty for failing to achieve a desired value. In financial risk management the function is precisely mapped to a monetary loss.
Loss Rank Mining
(LRM)
Modern object detectors usually suffer from low accuracy issues, as foregrounds always drown in tons of backgrounds and become hard examples during training. Compared with those proposal-based ones, real-time detectors are in far more serious trouble since they renounce the use of region-proposing stage which is used to filter a majority of backgrounds for achieving real-time rates. Though foregrounds as hard examples are in urgent need of being mined from tons of backgrounds, a considerable number of state-of-the-art real-time detectors, like YOLO series, have yet to profit from existing hard example mining methods, as using these methods need detectors fit series of prerequisites. In this paper, we propose a general hard example mining method named Loss Rank Mining (LRM) to fill the gap. LRM is a general method for real-time detectors, as it utilizes the final feature map which exists in all real-time detectors to mine hard examples. By using LRM, some elements representing easy examples in final feature map are filtered and detectors are forced to concentrate on hard examples during training. Extensive experiments validate the effectiveness of our method. With our method, the improvements of YOLOv2 detector on auto-driving related dataset KITTI and more general dataset PASCAL VOC are over 5% and 2% mAP, respectively. In addition, LRM is the first hard example mining strategy which could fit YOLOv2 perfectly and make it better applied in series of real scenarios where both real-time rates and accurate detection are strongly demanded.
Lotka’s Law Lotka’s law, named after Alfred J. Lotka, is one of a variety of special applications of Zipf’s law. It describes the frequency of publication by authors in any given field. It states that the number of authors making n contributions is about 1/n^{a} of those making one contribution, where a nearly always equals two. More plainly, the number of authors publishing a certain number of articles is a fixed ratio to the number of authors publishing a single article. As the number of articles published increases, authors producing that many publications become less frequent. There are 1/4 as many authors publishing two articles within a specified time period as there are single-publication authors, 1/9 as many publishing three articles, 1/16 as many publishing four articles, etc. Though the law itself covers many disciplines, the actual ratios involved (as a function of ‘a’) are very discipline-specific.
LotkasLaw
Lottery Ticket Hypothesis Recent work on neural network pruning indicates that, at training time, neural networks need to be significantly larger in size than is necessary to represent the eventual functions that they learn. This paper articulates a new hypothesis to explain this phenomenon. This conjecture, which we term the ‘lottery ticket hypothesis,’ proposes that successful training depends on lucky random initialization of a smaller subcomponent of the network. Larger networks have more of these ‘lottery tickets,’ meaning they are more likely to luck out with a subcomponent initialized in a configuration amenable to successful optimization. This paper conducts a series of experiments with XOR and MNIST that support the lottery ticket hypothesis. In particular, we identify these fortuitously-initialized subcomponents by pruning low-magnitude weights from trained networks. We then demonstrate that these subcomponents can be successfully retrained in isolation so long as the subnetworks are given the same initializations as they had at the beginning of the training process. Initialized as such, these small networks reliably converge successfully, often faster than the original network at the same level of accuracy. However, when these subcomponents are randomly reinitialized or rearranged, they perform worse than the original network. In other words, large networks that train successfully contain small subnetworks with initializations conducive to optimization. The lottery ticket hypothesis and its connection to pruning are a step toward developing architectures, initializations, and training strategies that make it possible to solve the same problems with much smaller networks.
Louvain Method Our method, that we call Louvain Method (because, even though the co-authors now hold positions in Paris, London and Louvain, the method was devised when they all were in Louvain), outperforms other methods in terms of computation time, which allows us to analyze networks of unprecedented size (e.g. the analysis of a typical network of 2 million nodes only takes 2 minutes). The Louvain method has also been to shown to be very accurate by focusing on ad-hoc networks with known community structure. Moreover, due to its hierarchical structure, which is reminiscent of renormalization methods, it allows to look at communities at different resolutions.
“Community Detection”
Louvain Modularity The Louvain Method for community detection is a method to extract communities from large networks created by Vincent Blondel. The method is a greedy optimization method that appears to run in time O(n log n).
http://…/0803.0476v2.pdf
Lovasz Convolutional Network
(LCN)
Semi-supervised learning on graph structured data has received significant attention with the recent introduction of graph convolution networks (GCN). While traditional methods have focused on optimizing a loss augmented with Laplacian regularization framework, GCNs perform an implicit Laplacian type regularization to capture local graph structure. In this work, we propose Lovasz convolutional network (LCNs) which are capable of incorporating global graph properties. LCNs achieve this by utilizing Lovasz’s orthonormal embeddings of the nodes. We analyse local and global properties of graphs and demonstrate settings where LCNs tend to work better than GCNs. We validate the proposed method on standard random graph models such as stochastic block models (SBM) and certain community structure based graphs where LCNs outperform GCNs and learn more intuitive embeddings. We also perform extensive binary and multi-class classification experiments on real world datasets to demonstrate LCN’s effectiveness. In addition to simple graphs, we also demonstrate the use of LCNs on hypergraphs by identifying settings where they are expected to work better than GCNs.
Low Algebraic Dimension Matrix Completion
(LADMC)
In the low rank matrix completion (LRMC) problem, the low rank assumption means that the columns (or rows) of the matrix to be completed are points on a low-dimensional linear algebraic variety. This paper extends this thinking to cases where the columns are points on a low-dimensional nonlinear algebraic variety, a problem we call Low Algebraic Dimension Matrix Completion (LADMC). Matrices whose columns belong to a union of subspaces (UoS) are an important special case. We propose a LADMC algorithm that leverages existing LRMC methods on a tensorized representation of the data. For example, a second-order tensorization representation is formed by taking the outer product of each column with itself, and we consider higher order tensorizations as well. This approach will succeed in many cases where traditional LRMC is guaranteed to fail because the data are low-rank in the tensorized representation but not in the original representation. We also provide a formal mathematical justification for the success of our method. In particular, we show bounds of the rank of these data in the tensorized representation, and we prove sampling requirements to guarantee uniqueness of the solution. Interestingly, the sampling requirements of our LADMC algorithm nearly match the information theoretic lower bounds for matrix completion under a UoS model. We also provide experimental results showing that the new approach significantly outperforms existing state-of-the-art methods for matrix completion in many situations.
Low Complexity Neural Network
(LCNN)
Modern neural network architectures for large-scale learning tasks have substantially higher model complexities, which makes understanding, visualizing and training these architectures difficult. Recent contributions to deep learning techniques have focused on architectural modifications to improve parameter efficiency and performance. In this paper, we derive a continuous and differentiable error functional for a neural network that minimizes its empirical error as well as a measure of the model complexity. The latter measure is obtained by deriving a differentiable upper bound on the Vapnik-Chervonenkis (VC) dimension of the classifier layer of a class of deep networks. Using standard backpropagation, we realize a training rule that tries to minimize the error on training samples, while improving generalization by keeping the model complexity low. We demonstrate the effectiveness of our formulation (the Low Complexity Neural Network – LCNN) across several deep learning algorithms, and a variety of large benchmark datasets. We show that hidden layer neurons in the resultant networks learn features that are crisp, and in the case of image datasets, quantitatively sharper. Our proposed approach yields benefits across a wide range of architectures, in comparison to and in conjunction with methods such as Dropout and Batch Normalization, and our results strongly suggest that deep learning techniques can benefit from model complexity control methods such as the LCNN learning rule.
Low Dimensional Manifold Regularized Neural Network
(LDMNet)
Deep neural networks have proved very successful on archetypal tasks for which large training sets are available, but when the training data are scarce, their performance suffers from overfitting. Many existing methods of reducing overfitting are data-independent, and their efficacy is often limited when the training set is very small. Data-dependent regularizations are mostly motivated by the observation that data of interest lie close to a manifold, which is typically hard to parametrize explicitly and often requires human input of tangent vectors. These methods typically only focus on the geometry of the input data, and do not necessarily encourage the networks to produce geometrically meaningful features. To resolve this, we propose a new framework, the Low-Dimensional-Manifold-regularized neural Network (LDMNet), which incorporates a feature regularization method that focuses on the geometry of both the input data and the output features. In LDMNet, we regularize the network by encouraging the combination of the input data and the output features to sample a collection of low dimensional manifolds, which are searched efficiently without explicit parametrization. To achieve this, we directly use the manifold dimension as a regularization term in a variational functional. The resulting Euler-Lagrange equation is a Laplace-Beltrami equation over a point cloud, which is solved by the point integral method without increasing the computational complexity. We demonstrate two benefits of LDMNet in the experiments. First, we show that LDMNet significantly outperforms widely-used network regularizers such as weight decay and DropOut. Second, we show that LDMNet can be designed to extract common features of an object imaged via different modalities, which proves to be very useful in real-world applications such as cross-spectral face recognition.
Lowest Posterior Loss
(LPL)
This paper defines intrinsic credible regions, a method to produce objective Bayesian credible regions which only depends on the assumed model and the available data. Lowest posterior loss (LPL) regions are defined as Bayesian credible regions which contain values of minimum posterior expected loss: they depend both on the loss function and on the prior specification. An invariant, information-theory based loss function, the intrinsic discrepancy is argued to be appropriate for scientific communication. Intrinsic credible regions are the lowest posterior loss regions with respect to the intrinsic discrepancy loss and the appropriate reference prior. The proposed procedure is completely general, and it is invariant under both reparametrization and marginalization. The exact derivation of intrinsic credible regions often requires numerical integration, but good analytical approximations are provided. Special attention is given to one-dimensional intrinsic credible intervals; their coverage properties show that they are always approximate (and sometimes exact) frequentist confidence intervals.
Lowest Posterior Loss Interval
(LPLI)
The Lowest Posterior Loss (LPL) interval (Bernardo, 2005), or LPLI, is a probability interval based on intrinsic discrepancy loss between prior and posterior distributions. The expected posterior loss is the loss associated with using a particular value theta[i] in theta of the parameter as the unknown true value of theta (Bernardo, 2005). Parameter values with smaller expected posterior loss should always be preferred. The LPL interval includes a region in which all parameter values have smaller expected posterior loss than those outside the region. Although any loss function could be used, the loss function should be invariant under reparameterization. Any intrinsic loss function is invariant under reparameterization, but not necessarily invariant under one-to-one transformations of data x. When a loss function is also invariant under one-to-one transformations, it is usually also invariant when reduced to a sufficient statistic. Only an intrinsic loss function that is invariant when reduced to a sufficient statistic should be considered. The intrinsic discrepancy loss is easily a superior loss function to the overused quadratic loss function, and is more appropriate than other popular measures, such as Hellinger distance, Kullback-Leibler divergence (KLD), and Jeffreys logarithmic divergence. The intrinsic discrepancy loss is also an information-theory related divergence measure. Intrinsic discrepancy loss is a symmetric, non-negative loss function, and is a continuous, convex function. Intrinsic discrepancy loss was introduced by Bernardo and Rueda (2002) in a different context: hypothesis testing. Formally, it is: delta f(p[2],p[1]) = min[kappa(p[2] | p[1]), kappa(p[1] | p[2])] where delta is the discrepancy, kappa is the KLD, and p[1] and p[2] are the probability distributions. The intrinsic discrepancy loss is the loss function, and the expected posterior loss is the mean of the directed divergences. The LPL interval is also called an intrinsic credible interval or intrinsic probability interval, and the area inside the interval is often called an intrinsic credible region or intrinsic probability region. In practice, whether a reference prior or weakly informative prior (WIP) is used, the LPL interval is usually very close to the HPD interval, though the posterior losses may be noticeably different. If LPL used a zero-one loss function, then the HPD interval would be produced. An advantage of the LPL interval over HPD interval (see p.interval) is that the LPL interval is invariant to reparameterization. This is due to the invariant reparameterization property of reference priors. The quantile-based probability interval is also invariant to reparameterization. The LPL interval enjoys the same advantage as the HPD interval does over the quantile-based probability interval: it does not produce equal tails when inappropriate. Compared with probability intervals, the LPL interval is slightly less convenient to calculate. Although the prior distribution is specified within the Model specification function, the user must specify it for the LPL.interval function as well. A comparison of the quantile-based probability interval, HPD interval, and LPL interval is available here: http://…/credible.
Low-pass Recurrent Neural Network Reinforcement learning (RL) agents performing complex tasks must be able to remember observations and actions across sizable time intervals. This is especially true during the initial learning stages, when exploratory behaviour can increase the delay between specific actions and their effects. Many new or popular approaches for learning these distant correlations employ backpropagation through time (BPTT), but this technique requires storing observation traces long enough to span the interval between cause and effect. Besides memory demands, learning dynamics like vanishing gradients and slow convergence due to infrequent weight updates can reduce BPTT’s practicality; meanwhile, although online recurrent network learning is a developing topic, most approaches are not efficient enough to use as replacements. We propose a simple, effective memory strategy that can extend the window over which BPTT can learn without requiring longer traces. We explore this approach empirically on a few tasks and discuss its implications.
Low-Rank Kernel Subspace Clustering Most state-of-the-art subspace clustering methods only work with linear (or affine) subspaces. In this paper, we present a kernel subspace clustering method that can handle non-linear models. While an arbitrary kernel can non-linearly map data into high-dimensional Hilbert feature space, the data in the resulting feature space are very unlikely to have the desired subspace structures. By contrast, we propose to learn a low-rank kernel mapping, with which the mapped data in feature space are not only low-rank but also self-expressive, such that the low-dimensional subspace structures are present and manifested in the high-dimensional feature space. We have evaluated the proposed method extensively on both motion segmentation and image clustering benchmarks, and obtained superior results, outperforming the kernel subspace clustering method that uses standard kernels~\cite{patel2014kernel} and other state-of-the-art linear subspace clustering methods.
Low-Shot Transfer Detector
(LSTD)
Recent advances in object detection are mainly driven by deep learning with large-scale detection benchmarks. However, the fully-annotated training set is often limited for a target detection task, which may deteriorate the performance of deep detectors. To address this challenge, we propose a novel low-shot transfer detector (LSTD) in this paper, where we leverage rich source-domain knowledge to construct an effective target-domain detector with very few training examples. The main contributions are described as follows. First, we design a flexible deep architecture of LSTD to alleviate transfer difficulties in low-shot detection. This architecture can integrate the advantages of both SSD and Faster RCNN in a unified deep framework. Second, we introduce a novel regularized transfer learning framework for low-shot detection, where the transfer knowledge (TK) and background depression (BD) regularizations are proposed to leverage object knowledge respectively from source and target domains, in order to further enhance fine-tuning with a few target images. Finally, we examine our LSTD on a number of challenging low-shot detection experiments, where LSTD outperforms other state-of-the-art approaches. The results demonstrate that LSTD is a preferable deep detector for low-shot scenarios.
Lp Space In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz (Riesz 1910). Lp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. Lebesgue spaces have applications in physics, statistics, finance, engineering, and other disciplines.
Lua Lua is a powerful, efficient, lightweight, embeddable scripting language. It supports procedural programming, object-oriented programming, functional programming, data-driven programming, and data description. Lua combines simple procedural syntax with powerful data description constructs based on associative arrays and extensible semantics. Lua is dynamically typed, runs by interpreting bytecode with a register-based virtual machine, and has automatic memory management with incremental garbage collection, making it ideal for configuration, scripting, and rapid prototyping.
Luigi Luigi is a Python module that helps you build complex pipelines of batch jobs. It handles dependency resolution, workflow management, visualization etc. It also comes with Hadoop support built in.
Luigi is an open source Python-based data framework for building data pipelines. Instead of using an XML/YAML configuration of some sort, all the jobs and their dependencies are written as Python programs. Because it’s Python, developers can backtrack to figure out exactly how data is processed.
The framework makes it easier to build large data pipelines, with built-in checkpointing, failure recovery, parallel execution, command line integration, etc. Since it’s a Python program, any Python library assets can be reused. The Luigi framework itself is a couple of thousand lines, so it’s also easy to understand the entire mechanism.
Facebook built a similar internal system called Dataswarm (Video), which allows developers to manage the entire data pipeline on Git + Python.
While Luigi was originally invented for Spotify’s internal needs, companies such as Foursquare, Stripe, and Asana are using it in production.
Lurking Variable Lurking variables represent hidden information, and preclude a full understanding of phenomena of interest. Detection is usually based on serendipity — visual detection of unexplained, systematic variation. However, these approaches are doomed to fail if the lurking variables do not vary.
Lyapunov Neural Network Learning algorithms have shown considerable prowess in simulation by allowing robots to adapt to uncertain environments and improve their performance. However, such algorithms are rarely used in practice on safety-critical systems, since the learned policy typically does not yield any safety guarantees and thus the required exploration may cause physical harm to the robot or its environment. In this paper, we present a method to learn accurate safety certificates for nonlinear, closed-loop dynamic systems. Specifically, we construct a neural network Lyapunov function and a training algorithm that adapts it to the shape of the largest safe region in the state space. The algorithm relies only on knowledge of inputs and outputs of the dynamics, rather than on any specific model structure. We demonstrate our method by learning the safe region of attraction for a simulated inverted pendulum. Furthermore, we discuss how our method can be used in safe learning algorithms together with statistical models of dynamic systems.
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