BabelNet BabelNet is a multilingual lexicalized semantic network and ontology developed at the Linguistic Computing Laboratory in the Department of Computer Science of the Sapienza University of Rome. BabelNet was automatically created by linking the largest multilingual Web encyclopedia, Wikipedia, to the most popular computational lexicon of the English language, WordNet. The integration is performed by means of an automatic mapping and by filling in lexical gaps in resource-poor languages with the aid of statistical machine translation. The result is an ‘encyclopedic dictionary’ that provides concepts and named entities lexicalized in many languages and connected with large amounts of semantic relations. Additional lexicalizations and definitions are added by linking to free-license wordnets, OmegaWiki, the English Wiktionary and Wikidata. Similarly to WordNet, BabelNet groups words in different languages into sets of synonyms, called Babel synsets. For each Babel synset, BabelNet provides short definitions (called glosses) in many languages harvested from both WordNet and Wikipedia. BabelNet Backpropagation Backpropagation, an abbreviation for “backward propagation of errors”, is a common method of training artificial neural networks used in conjunction with an optimization method such as gradient descent. The method calculates the gradient of a loss function with respects to all the weights in the network. The gradient is fed to the optimization method which in turn uses it to update the weights, in an attempt to minimize the loss function. Backpropagation requires a known, desired output for each input value in order to calculate the loss function gradient. It is therefore usually considered to be a supervised learning method, although it is also used in some unsupervised networks such as autoencoders. It is a generalization of the delta rule to multi-layered feedforward networks, made possible by using the chain rule to iteratively compute gradients for each layer. Backpropagation requires that the activation function used by the artificial neurons (or “nodes”) be differentiable. Backpropogation Through Time(BPTT) ➘ “Predictive State Recurrent Neural Networks” Backtesting Backtesting is jargon used in financial industries to refer to testing a trading strategy or predictive model using existing historic data. Backtesting is a special type of cross-validation applied to time series data. Backwards Analysis The idea of backwards analysis (or backward analysis) is a technique to analyze randomized algorithms by imagining as if it was running backwards in time, from output to input. Most of the more interesting applications of backward analysis are in Computational Geometry, but nevertheless, there are some other applications that are interesting and we survey some of them here. Bag Of Centroids Model https://…/Word2Vec_BagOfCentroids.py Bag of Little Bootstraps(BLB) Bag of Little Bootstraps (BLB), a new procedure which incorporates features of both the bootstrap and subsampling to yield a robust, computationally efficient means of assessing the quality of estimators. BLB is well suited to modern parallel and distributed computing architectures and furthermore retains the generic applicability and statistical efficiency of the bootstrap. We demonstrate BLB’s favorable statistical performance via a theoretical analysis elucidating the procedure’s properties, as well as a simulation study comparing BLB to the bootstrap, the out of bootstrap, and subsampling. Introduction to Bag of Little Bootstrap Bag Of Words Model The bag-of-words model is a simplifying representation used in natural language processing and information retrieval (IR). In this model, a text (such as a sentence or a document) is represented as the bag (multiset) of its words (matrix), disregarding grammar and even word order but keeping multiplicity. The bag-of-words model is commonly used in methods of document classification, where the (frequency of) occurrence of each word is used as a feature for training a classifier. Bagging Hierarchical Clustering Bagging (bootstrap aggregating) is usually used with supervised methods to improve their stability and accuracy. The idea is to bootstrap the sample, build a predictive model on each bootstrapped sample and then combine the results to produce for classification a vote on the predicted class and for the continuous case an average prediction. If we bootstrap sample our data and build a separate hierarchical clustering solution on each sample can we then combine the results to produce a more stable clustering solution. Banzhaf Random Forests(BRF) Random forests are a type of ensemble method which makes predictions by combining the results of several independent trees. However, the theory of random forests has long been outpaced by their application. In this paper, we propose a novel random forests algorithm based on cooperative game theory. Banzhaf power index is employed to evaluate the power of each feature by traversing possible feature coalitions. Unlike the previously used information gain rate of information theory, which simply chooses the most informative feature, the Banzhaf power index can be considered as a metric of the importance of each feature on the dependency among a group of features. More importantly, we have proved the consistency of the proposed algorithm, named Banzhaf random forests (BRF). This theoretical analysis takes a step towards narrowing the gap between the theory and practice of random forests for classification problems. Experiments on several UCI benchmark data sets show that BRF is competitive with state-of-the-art classifiers and dramatically outperforms previous consistent random forests. Particularly, it is much more efficient than previous consistent random forests. Barnard’s Test In statistics, Barnard’s test is an exact test used in the analysis of contingency tables. The test was first published by George Alfred Barnard (1945, 1947) who claimed this test is a more powerful alternative than Fisher’s exact test for 2×2 contingency tables. A previous barrier to the widespread use of Barnard’s test was likely the computational difficulty of calculating the p-value; nowadays, computers can implement Barnard’s test. Basic Linear Algebra Subprograms(BLAS) The Basic Linear Algebra Subprograms (BLAS) are a specified set of low-level kernel subroutines that perform common linear algebra operations such as copying, vector scaling, vector dot products, linear combinations, and matrix multiplication. They were first published as a Fortran library in 1979 and are still used as a building block in higher-level math programming languages and libraries, including LINPACK, LAPACK, MATLAB, Mathematica, NumPy and R. BLAS subroutines are a de facto standard API for linear algebra libraries and routines. Several BLAS library implementations have been tuned for specific computer architectures. Highly optimized implementations have been developed by hardware vendors such as Intel and AMD, as well as by other authors, e.g. GotoBLAS and ATLAS (a portable self-optimizing BLAS). The LINPACK and HPL benchmarks rely heavily on DGEMM, a BLAS subroutine, for its performance measurements. Basic Recurrent Neural Network Model(bRNN) We present a model of a basic recurrent neural network (or bRNN) that includes a separate linear term with a slightly ‘stable’ fixed matrix to guarantee bounded solutions and fast dynamic response. We formulate a state space viewpoint and adapt the constrained optimization Lagrange Multiplier (CLM) technique and the vector Calculus of Variations (CoV) to derive the (stochastic) gradient descent. In this process, one avoids the commonly used re-application of the circular chain-rule and identifies the error back-propagation with the co-state backward dynamic equations. We assert that this bRNN can successfully perform regression tracking of time-series. Moreover, the ‘vanishing and exploding’ gradients are explicitly quantified and explained through the co-state dynamics and the update laws. The adapted CoV framework, in addition, can correctly and principally integrate new loss functions in the network on any variable and for varied goals, e.g., for supervised learning on the outputs and unsupervised learning on the internal (hidden) states. Bass Diffusion Model The Bass Model or Bass Diffusion Model was developed by Frank Bass and it consists of a simple differential equation that describes the process of how new products get adopted in a population. The model presents a rationale of how current adopters and potential adopters of a new product interact. The basic premise of the model is that adopters can be classified as innovators or as imitators and the speed and timing of adoption depends on their degree of innovativeness and the degree of imitation among adopters. The Bass model has been widely used in forecasting, especially new products’ sales forecasting and technology forecasting. Mathematically, the basic Bass diffusion is a Riccati equation with constant coefficients. Frank Bass published his paper “A new product growth for model consumer durables” in 1969 whose title indeed contained a typographical error. Prior to this, Everett Rogers published Diffusion of Innovations, a highly influential work that described the different stages of product adoption. Bass contributed some mathematical ideas to the concept. Batch Normalization Training Deep Neural Networks is complicated by the fact that the distribution of each layer’s inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization. It also acts as a regularizer, in some cases eliminating the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.9% top-5 validation error (and 4.8% test error), exceeding the accuracy of human raters. Batch-Expansion Training(BET) We propose Batch-Expansion Training (BET), a framework for running a batch optimizer on a gradually expanding dataset. As opposed to stochastic approaches, batches do not need to be resampled i.i.d. at every iteration, thus making BET more resource efficient in a distributed setting, and when disk-access is constrained. Moreover, BET can be easily paired with most batch optimizers, does not require any parameter-tuning, and compares favorably to existing stochastic and batch methods. We show that when the batch size grows exponentially with the number of outer iterations, BET achieves optimal $\tilde{O}(1/\epsilon)$ data-access convergence rate for strongly convex objectives. Battery Reduction Battery reduction is used to select a subset of m variables from an original set of n variables (m < n) that reproduce a large proportion of the variance in the original set of n variables. There are a number of procedures for performing battery reduction analysis. A popular method involves performing a principal components analysis first to select m components, which account for the salient variance in the original data. Gram-Schmidt orthogonal rotations are then performed to determine the m variables that account for the largest proportion of variance. Baum-Welch Algorithm In electrical engineering, computer science, statistical computing and bioinformatics, the Baum-Welch algorithm is used to find the unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm and is named for Leonard E. Baum and Lloyd R. Welch. Bayes Factor In statistics, the use of Bayes factors is a Bayesian alternative to classical hypothesis testing. Bayesian model comparison is a method of model selection based on Bayes factors. Bayes factors provide a numerical value that quantifies how well a hypothesis predicts the empirical data relative to a competing hypothesis. For example, if the BF is 4, this indicates: ‘This empirical data is 4 times more probable if H1 were true than if H0 were true.’. Hence, evidence points towards H1. A BF of 1 means that data are equally likely to be occured under both hypotheses. In this case, it would be impossible to decide between both. http://…/a-short-taxonomy-of-bayes-factors Bayes Point Machine Kernel-classifiers comprise a powerful class of non-linear decision functions for binary classification. The support vector machine is an example of a learning algorithm for kernel classifiers that singles out the consistent classifier with the largest margin, i.e. minimal real-valued output on the training sample, within the set of consistent hypotheses, the so-called version space. We suggest the Bayes point machine as a well-founded improvement which approximates the Bayes-optimal decision by the centre of mass of version space. We present two algorithms to stochastically approximate the centre of mass of version space: a billiard sampling algorithm and a sampling algorithm based on the well known perceptron algorithm. It is shown how both algorithms can be extended to allow for soft-boundaries in order to admit training errors. Experimentally, we find that — for the zero training error case — Bayes point machines consistently outperform support vector machines on both surrogate data and real-world benchmark data sets. In the soft-boundary/soft-margin case, the improvement over support vector machines is shown to be reduced. Finally, we demonstrate that the realvalued output of single Bayes points on novel test points is a valid confidence measure and leads to a steady decrease in generalisation error when used as a rejection criterion. http://…/bayes%20point%20machine%20tutorial.aspx BayesDB BayesDB is a probabilistic programming platform that enables users to query the probable implications of their data as directly as SQL databases enable them to query the data itself. The default modeling assumptions that BayesDB makes are suitable for a broad class of problems, but statisticians can customize these assumptions when necessary. BayesDB also enables domain experts that lack statistical expertise to perform qualitative model checking and encode simple forms of qualitative prior knowledge. BayesDB: A probabilistic programming system for querying the probable implications of data BayesDB Bayesian Additive Regression Trees(BART) A Bayesian “sum-of-trees” model where each tree is constrained by a regularization prior to be a weak learner, and fitting and inference are accomplished via an iterative Bayesian backfitting MCMC algorithm that generates samples from a posterior. Effectively, BART is a nonparametric Bayesian regression approach which uses dimensionally adaptive random basis elements. Motivated by ensemble methods in general, and boosting algorithms in particular, BART is defined by a statistical model: a prior and a likelihood. This approach enables full posterior inference including point and interval estimates of the unknown regression function as well as the marginal effects of potential predictors. By keeping track of predictor inclusion frequencies, BART can also be used for model free variable selection. BayesTree,BART Bayesian Adjustment for Confounding(BAC) Bayesian Belief Network(BBN) A Bayesian belief network is a graphical representation of a probabilistic dependency model. It consists of a set of interconnected nodes, where each node represents a variable in the dependency model and the connecting arcs represent the causal relationships between these variables. Each node or variable may take one of a number of possible states or values. The belief in, or certainty of, each of these states is determined from the belief in each possible state of every node directly connected to it and its relationship with each of these nodes. The belief in each state of a node is updated whenever the belief in each state of any directly connected node changes. Bayesian Bootstrap Bootstrapping can be interpreted in a Bayesian framework using a scheme that creates new datasets through reweighting the initial data. http://…-parametric-bootstrap-as-a-bayesian-model http://…/1176345338 Bayesian Bridge Bridge regression is a regularized regression in which the regression coefficient’s prior is an exponential power distribution. BayesBridge Bayesian Causal Effect Estimation(BCEE) Estimating causal exposure effects in observational studies ideally requires the analyst to have a vast knowledge of the domain of application. Investigators often bypass difficulties related to the identification and selection of confounders through the use of fully adjusted outcome regression models. However, since such models likely contain more covariates than required, the variance of the regression coefficient for exposure may be unnecessarily large. Instead of using a fully adjusted model, model selection can be attempted. Most classical statistical model selection approaches, such as Bayesian model averaging, do not readily address causal effect estimation. We present a novel model averaged approach to causal inference, the Bayesian Causal Effect Estimation (BCEE) algorithm, which is motivated by the graphical framework for causal inference. BCEE aims to unbiasedly estimate the causal effect of a continuous exposure on a continuous outcome while being more efficient than a fully adjusted model. Bayesian Conditional Generative Adverserial Networks(BC-GAN) Traditional GANs use a deterministic generator function (typically a neural network) to transform a random noise input $z$ to a sample $\mathbf{x}$ that the discriminator seeks to distinguish. We propose a new GAN called Bayesian Conditional Generative Adversarial Networks (BC-GANs) that use a random generator function to transform a deterministic input $y’$ to a sample $\mathbf{x}$. Our BC-GANs extend traditional GANs to a Bayesian framework, and naturally handle unsupervised learning, supervised learning, and semi-supervised learning problems. Experiments show that the proposed BC-GANs outperforms the state-of-the-arts. Bayesian Decision Theory Bayesian decision theory is a fundamental statistical approach to the problem of pattern classification. It is considered the ideal case in which the probability structure underlying the categories is known perfectly. While this sort of stiuation rarely occurs in practice, it permits us to determine the optimal (Bayes) classifier against which we can compare all other classifiers. Moreover, in some problems it enables us to predict the error we will get when we generalize to novel patterns. This approach is based on quantifying the tradeoffs between various classification decisions using probability and the costs that accompany such decisions. It makes the assumption that the decision problem is posed in probabilistic terms, and that all of the relevant probability values are known. http://…/Bayesian_decision_theory http://…/bayesian.pdf Bayesian Estimation Bayesian Exponential Random Graph Models Bergm Bayesian Hierarchical Matrix Factorization(BHMF) BHPMF Bayesian Highest Posterior Density(HPD) Bayesian Information Criterion(BIC) In statistics, the Bayesian information criterion (BIC) or Schwarz criterion (also SBC, SBIC) is a criterion for model selection among a finite set of models. It is based, in part, on the likelihood function and it is closely related to the Akaike information criterion (AIC). When fitting models, it is possible to increase the likelihood by adding parameters, but doing so may result in overfitting. Both BIC and AIC resolve this problem by introducing a penalty term for the number of parameters in the model; the penalty term is larger in BIC than in AIC. The BIC was developed by Gideon E. Schwarz, who gave a Bayesian argument for adopting it. Bayesian Kernel Projection Classifier(BKPC) Bayesian kernel projection classifier is a nonlinear multicategory classifier which performs the classification of the projections of the data to the principal axes of the feature space. A Gibbs sampler is implemented to find the posterior distributions of the parameters. BKPC Bayesian Latent Class Analysis Bayesian Linear Regression In statistics, Bayesian linear regression is an approach to linear regression in which the statistical analysis is undertaken within the context of Bayesian inference. When the regression model has errors that have a normal distribution, and if a particular form of prior distribution is assumed, explicit results are available for the posterior probability distributions of the model’s parameters. Bayesian Masking A common strategy for sparse linear regression is to introduce regularization, which eliminates irrelevant features by letting the corresponding weights be zeros. Regularization, however, often shrinks the estimator for relevant features, which leads incorrect feature selection. Motivated by the above issue, we propose Bayesian masking (BM), a sparse estimation method which imposes no regularization on the weights. The key concept of BM is to introduce binary latent variables that randomly mask features. Estimating the masking rates determines the relevances of the features automatically. We derive a variational Bayesian inference algorithm that maximizes a lower bound of the factorized information criterion (FIC), which is a recently-developed asymptotic evaluation of the marginal log-likelihood. We also propose reparametrization that accelerates the convergence. We demonstrate that BM outperforms Lasso and automatic relevance determination (ARD) in terms of the sparsity-shrinkage trade-off. Bayesian Model Averaging Bayesian Model Averaging is a technique designed to help account for the uncertainty inherent in the model selection process, something which traditional statistical analysis often neglects. By averaging over many different competing models, BMA incorporates model uncertainty into conclusions about parameters and prediction. BMA has been applied successfully to many statistical model classes including linear regression, generalized linear models, Cox regression models, and discrete graphical models, in all cases improving predictive performance. Bayesian Network(BN) A Bayesian network, Bayes network, belief network, Bayes(ian) model or probabilistic directed acyclic graphical model is a probabilistic graphical model (a type of statistical model) that represents a set of random variables and their conditional dependencies via a directed acyclic graph (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Bayesian Neural Network(BNN) The training of neural networks can be viewed as a problem of inference, which can be addressed from a Bayesian viewpoint. This perspective leads to a method, new to the field of particle physics, called Bayesian neural networks (BNN). A History of Bayesian Neural Networks Bayesian Nonparametric Model A Bayesian nonparametric model is a Bayesian model on an infinite-dimensional parameter space. The parameter space is typically chosen as the set of all possible solutions for a given learning problem. For example, in a regression problem the parameter space can be the set of continuous functions, and in a density estimation problem the space can consist of all densities. A Bayesian nonparametric model uses only a finite subset of the available parameter dimensions to explain a finite sample of observations, with the set of dimensions chosen depending on the sample, such that the effective complexity of the model (as measured by the number of dimensions used) adapts to the data. Classical adaptive problems, such as nonparametric estimation and model selection, can thus be formulated as Bayesian inference problems. Popular examples of Bayesian nonparametric models include Gaussian process regression, in which the correlation structure is refined with growing sample size, and Dirichlet process mixture models for clustering, which adapt the number of clusters to the complexity of the data. Bayesian nonparametric models have recently been applied to a variety of machine learning problems, including regression, classification, clustering, latent variable modeling, sequential modeling, image segmentation, source separation and grammar induction. Bayesian Passive-Aggressive Learning(BayesPA) Online Passive-Aggressive (PA) learning is an effective framework for performing max-margin online learning. But the deterministic formulation and estimated single large-margin model could limit its capability in discovering descriptive structures underlying complex data. This paper presents online Bayesian Passive-Aggressive (BayesPA) learning, which subsumes the online PA and extends naturally to incorporate latent variables and perform nonparametric Bayesian inference, thus providing great flexibility for explorative analysis. We apply BayesPA to topic modeling and derive efficient online learning algorithms for max-margin topic models. We further develop nonparametric methods to resolve the number of topics. Experimental results on real datasets show that our approaches significantly improve time efficiency while maintaining comparable results with the batch counterparts. Bayesian Tensor Factorization Linked to External Data(BaTFLED) The vast majority of current machine learning algorithms are designed to predict single responses or a vector of responses, yet many types of response are more naturally organized as matrices or higher-order tensor objects where characteristics are shared across modes. We present a new machine learning algorithm BaTFLED (Bayesian Tensor Factorization Linked to External Data) that predicts values in a three-dimensional response tensor using input features for each of the dimensions. BaTFLED uses a probabilistic Bayesian framework to learn projection matrices mapping input features for each mode into latent representations that multiply to form the response tensor. By utilizing a Tucker decomposition, the model can capture weights for interactions between latent factors for each mode in a small core tensor. Priors that encourage sparsity in the projection matrices and core tensor allow for feature selection and model regularization. This method is shown to far outperform elastic net and neural net models on ‘cold start’ tasks from data simulated in a three-mode structure. Additionally, we apply the model to predict dose-response curves in a panel of breast cancer cell lines treated with drug compounds that was used as a Dialogue for Reverse Engineering Assessments and Methods (DREAM) challenge. Bayesian Ying-Yang Learning Algorithm(BYY) Ying-Yang learning considers a learning system featured with two pathways between the external observation domain X and its inner representation domain R. The domain R and the pathway R→X is modeled by one subsystem system, while the domain X and the pathway X→R is modeled by another subsystem. From the view of the ancient Ying-Yang philosophy, the former is called Ying and the latter is called Yang, and the two coordinately form a Ying-Yang system, with the structure of Ying subject to a principle of compactness (least complexity) and the structure of Yang subject to a principle of proper vitality (matched dynamic range) with respect to the Ying. Moreover, all the rest unknowns in the Ying-Yang system are learned under the guidance of a Ying-Yang best harmony principle. http://…/index-pub-byy.html http://…/chapters-Xu03a.pdf Behavioral Analytics Behavioral Analytics is a subset of business analytics that focuses on how and why users of eCommerce platforms, online games, & web applications behave. While business analytics has a more broad focus on the who, what, where and when of business intelligence, behavioral analytics narrows that scope, allowing one to take seemingly unrelated data points in order to extrapolate, predict and determine errors and future trends. It takes a more holistic and human view of data, connecting individual data points to tell us not only what is happening, but also how and why it is happening. Behavioral analytics utilizes user data captured while the web application, game, or website is in use by analytic platforms like Google Analytics. Platform traffic data like navigation paths, clicks, social media interactions, purchasing decisions and marketing responsiveness is all recorded. Also, other more specific advertising metrics like click-to-conversion time, and comparisons between other metrics like the monetary value of an order and the amount of time spent on the site. These data points are then compiled and analyzed, whether by looking at the timeline progression from when a user first entered the platform until a sale was made, or what other products a user bought or looked at before this purchase. Behavioral analysis allows future actions and trends to be predicted based on all the data collected. Behavioral Change Point Analysis(BCPA) The Behavioral Change Point Analysis (BCPA) is a method of identifying hidden shifts in the underlying parameters of a time series, developed specifically to be applied to animal movement data which is irregularly sampled. Belief Functions The theory of belief functions provides a non-Bayesian way of using mathematical probability to quantify subjective judgements. Whereas a Bayesian assesses probabilities directly for the answer to a question of interest, a belief-function user assesses probabilities for related questions and then considers the implications of these probabilities for the question of interest. Belief Network see “Bayesian Network” or “Bayes Net” Belief Propagation Belief propagation, also known as sum-product message passing is a message passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields. It calculates the marginal distribution for each unobserved node, conditional on any observed nodes. Belief propagation is commonly used in artificial intelligence and information theory and has demonstrated empirical success in numerous applications including low-density parity-check codes, turbo codes, free energy approximation, and satisfiability. The algorithm was first proposed by Judea Pearl in 1982, who formulated this algorithm on trees, and was later extended to polytrees. It has since been shown to be a useful approximate algorithm on general graphs. Bellman Equation A Bellman equation, named after its discoverer, Richard Bellman, also known as a dynamic programming equation, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. It writes the value of a decision problem at a certain point in time in terms of the payoff from some initial choices and the value of the remaining decision problem that results from those initial choices. This breaks a dynamic optimization problem into simpler subproblems, as Bellman’s Principle of Optimality prescribes. The Bellman equation was first applied to engineering control theory and to other topics in applied mathematics, and subsequently became an important tool in economic theory. Almost any problem which can be solved using optimal control theory can also be solved by analyzing the appropriate Bellman equation. However, the term ‘Bellman equation’ usually refers to the dynamic programming equation associated with discrete-time optimization problems. In continuous-time optimization problems, the analogous equation is a partial differential equation which is usually called the Hamilton-Jacobi-Bellman equation. Benford’s Law Benford’s Law, also called the First-Digit Law, refers to the frequency distribution of digits in many (but not all) real-life sources of data. In this distribution, the number 1 occurs as the leading digit about 30% of the time, while larger numbers occur in that position less frequently: 9 as the first digit less than 5% of the time. Benford’s Law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution. Bent-Cable Regression We use the so-called bent-cable model to describe natural phenomena which exhibit a potentially sharp change in slope. The model comprises two linear segments, joined smoothly by a quadratic bend. The class of bent cables includes, as a limiting case, the popular piecewise-linear model (with a sharp kink), otherwise known as the broken stick. Associated with bent-cable regression is the estimation of the bendwidth parameter, through which the abruptness of the underlying transition may be assessed. Berkeley Data Analytics Stack(BDAS) BDAS, the Berkeley Data Analytics Stack, is an open source software stack that integrates software components being built by the Berkeley AMPLab to make sense of Big Data. Bessels Correction In statistics, Bessel’s correction, named after Friedrich Bessel, is the use of n – 1 instead of n in the formula for the sample variance and sample standard deviation, where n is the number of observations in a sample. This corrects the bias in the estimation of the population variance, and some (but not all) of the bias in the estimation of the population standard deviation, but often increases the mean squared error in these estimations. Best Friends For Ever(BFF) Graphs form a natural model for relationships and interactions between entities, for example, between people in social and cooperation networks, servers in computer networks,or tags and words in documents and tweets. But, which of these relationships or interactions are the most lasting ones? In this paper, given a set of graph snapshots, which may correspond to the state of a dynamic graph at different time instances, we look at the problem of identifying the set of nodes that are the most densely connected at all snapshots. We call this problem the Best Friends For Ever (Bff) problem. We provide definitions for density over multiple graph snapshots, that capture different semantics of connectedness over time, and we study the corresponding variants of the Bff problem. We then look at the On-Off Bff (O2Bff) problem that relaxes the requirement of nodes being connected in all snapshots, and asks for the densest set of nodes in at least k of a given set of graph snapshots. We show that this problem is NP-complete for all definitions of density, and we propose a set of efficient algorithms. Finally, we present experiments with synthetic and real datasets that show both the efficiency of our algorithms and the usefulness of the Bff and the O2Bff problems. Best Linear Unbiased Estimator(BLUE) In statistics, the Gauss-Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator (BLUE) of the coefficients is given by the ordinary least squares (OLS) estimator. Here ‘best’ means giving the lowest variance of the estimate, as compared to other unbiased, linear estimators. The errors don’t need to be normal, nor do they need to be independent and identically distributed (only uncorrelated and homoscedastic). The hypothesis that the estimator be unbiased cannot be dropped, since otherwise estimators better than OLS exist. See for examples the James-Stein estimator (which also drops linearity) or ridge regression. Best Linear Unbiased Prediction(BLUP) In statistics, best linear unbiased prediction (BLUP) is used in linear mixed models for the estimation of random effects. BLUP was derived by Charles Roy Henderson in 1950 but the term ‘best linear unbiased predictor’ (or ‘prediction’) seems not to have been used until 1962. ‘Best linear unbiased predictions’ (BLUPs) of random effects are similar to best linear unbiased estimates (BLUEs) () of fixed effects. The distinction arises because it is conventional to talk about estimating fixed effects but predicting random effects, but the two terms are otherwise equivalent. (This is a bit strange since the random effects have already been ‘realized’ − they already exist. The use of the term ‘prediction’ may be because in the field of animal breeding in which Henderson worked, the random effects were usually genetic merit, which could be used to predict the quality of offspring. However, the equations for the ‘fixed’ effects and for the random effects are different. In practice, it is often the case that the parameters associated with the random effect(s) term(s) are unknown; these parameters are the variances of the random effects and residuals. Typically the parameters are estimated and plugged into the predictor, leading to the Empirical Best Linear Unbiased Predictor (EBLUP). Notice that by simply plugging in the estimated parameter into the predictor, additional variability is unaccounted for, leading to overly optimistic prediction variances for the EBLUP. Best linear unbiased predictions are similar to empirical Bayes estimates of random effects in linear mixed models, except that in the latter case, where weights depend on unknown values of components of variance, these unknown variances are replaced by sample-based estimates. Best-Worst Scaling Best-Worst Scaling (BWS) can be a method of data collection, and/or a theory of how respondents provide top and bottom ranked items from a list. BWS is increasingly used to obtain more choice data from individuals and/or to understand choice processes. The three casesof BWS are described, together with the intuition behind the models that are applied in each case. A summary of the main theoretical results is provided, including an exposition of the possible theoretical relationships between estimates from the di¤erent cases, and of the theoretical properties of best minus worst scores.BWS data can be analysed using relatively simple extensions to maximum-likelihood based methods used in discrete choice experiments. These are summarised, before the benets of simple functions of the best and Beta Regression How should we one perform a regression analysis in which the dependent variable is restricted to the standard unit interval such as rates and proportions? Ferrari and Cribari-Neto, 2004 proposed a regression model for continuous variates that assume values in the standard unit interval, e.g., rates, proportions, or concentrations indices. The model is based on the assumption that the response is beta-distributed, they called their model the beta regression model. The regression parameters are interpretable in terms of the mean of y (the variable of interest) and the model is naturally heteroskedastic and easily accommodates asymmetries. A variant of the beta regression model that allows for nonlinearities and variable dispersion was proposed by Simas et al., 2010. zoib: An R package for Bayesian Inference for Beta Regression and Zero/One Inflated Beta Regression A Short Course in Beta Regression Models Bhattacharyya Distance In statistics, the Bhattacharyya distance measures the similarity of two discrete or continuous probability distributions. It is closely related to the Bhattacharyya coefficient which is a measure of the amount of overlap between two statistical samples or populations. Both measures are named after Anil Kumar Bhattacharya, a statistician who worked in the 1930s at the Indian Statistical Institute. The coefficient can be used to determine the relative closeness of the two samples being considered. It is used to measure the separability of classes in classification and it is considered to be more reliable than the Mahalanobis distance, as the Mahalanobis distance is a particular case of the Bhattacharyya distance when the standard deviations of the two classes are the same. Therefore, when two classes have similar means but different standard deviations, the Mahalanobis distance would tend to zero, however, the Bhattacharyya distance would grow depending on the difference between the standard deviations. Bias of an Estimator / Unbiasedness In statistics, the bias (or bias function) of an estimator is the difference between this estimator’s expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. Otherwise the estimator is said to be biased. In statistics, “bias” is an objective statement about a function, and while not a desired property, it is not pejorative, unlike the ordinary English use of the term “bias”. Bias/Variance Tradeoff In machine learning, the bias-variance dilemma or bias-variance tradeoff is the problem of simultaneously minimizing the bias (how accurate a model is across different training sets) and variance of the model error (how sensitive the model is to small changes in training set). This tradeoff applies to all forms of supervised learning: classification, function fitting, and structured output learning. It has also been invoked to explain the effectiveness of heuristics in human learning. BiBit Binary datasets represent a compact and simple way to store data about the relationships between a group of objects and their possible properties. In the last few years, different biclustering algorithms have been specially developed to be applied to binary datasets. Several approaches based on matrix factorization, suffix trees or divide-and-conquer techniques have been proposed to extract useful biclusters from binary data, and these approaches provide information about the distribution of patterns and intrinsic correlations. A novel approach to extracting biclusters from binary datasets, BiBit, is introduced here. The results obtained from different experiments with synthetic data reveal the excellent performance and the robustness of BiBit to density and size of input data. Also, BiBit is applied to a central nervous system embryonic tumor gene expression dataset to test the quality of the results. A novel gene expression preprocessing methodology, based on expression level layers, and the selective search performed by BiBit, based on a very fast bit-pattern processing technique, provide very satisfactory results in quality and computational cost. The power of biclustering in finding genes involved simultaneously in different cancer processes is also shown. Finally, a comparison with Bimax, one of the most cited binary biclustering algorithms, shows that BiBit is faster while providing essentially the same results. ➘ “Biclustering” BiBitR Biclustering Biclustering, co-clustering, or two-mode clustering is a data mining technique which allows simultaneous clustering of the rows and columns of a matrix. Big Data “Big Data” is the term for a collection of data sets so large and complex that it becomes difficult to process using on-hand database management tools or traditional data processing applications. The challenges include capture, curation, storage, search, sharing, transfer, analysis and visualization. Big Data Analytics(BDA) Big data analytics refers to the process of collecting, organizing and analyzing large sets of data (“big data”) to discover patterns and other useful information. Not only will big data analytics help you to understand the information contained within the data, but it will also help identify the data that is most important to the business and future business decisions. Big data analysts basically want the knowledge that comes from analyzing the data. Big Data Discovery Big Data Discovery = {Big Data, Data Discovery, Data Science} Big Data Management(BDM) Big Data Management (BDM), an amalgam of old and new best practices, skills, teams, data types, and home-grown or vendor-built functionality. All of these are expanding and realigning so that businesses can fully leverage big data, not merely manage it. At the same time, big data must eventually find a permanent place in enterprise data management. BDM is well worth doing because managing big data leads to a number of benefits. According to this report’s survey, the business and technology tasks that improve most are analytic insights, the completeness of analytic data sets, business value drawn from big data, and all sales and marketing activities. BDM also has challenges, and common barriers include low organizational maturity relative to big data, weak business support, and the need to learn new technology approaches. Big O Notation In mathematics, big O notation describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann-Landau notation (after Edmund Landau and Paul Bachmann), or asymptotic notation. In computer science, big O notation is used to classify algorithms by how they respond (e.g., in their processing time or working space requirements) to changes in input size. In analytic number theory, it is used to estimate the ‘error committed’ while replacing the asymptotic size, or asymptotic mean size, of an arithmetical function, by the value, or mean value, it takes at a large finite argument. A famous example is the problem of estimating the remainder term in the prime number theorem. Big O notation characterizes functions according to their growth rates: different functions with the same growth rate may be represented using the same O notation. The letter O is used because the growth rate of a function is also referred to as order of the function. A description of a function in terms of big O notation usually only provides an upper bound on the growth rate of the function. Associated with big O notation are several related notations, using the symbols o, Ω, ω, and Θ, to describe other kinds of bounds on asymptotic growth rates. Big O notation is also used in many other fields to provide similar estimates. Big Workflow Big Workflow is an industry term coined by Adaptive Computing that accelerates insights by more efficiently processing intense simulations and big data analysis. Adaptive Computing’s Big Workflow solution derives it name from its ability to solve big data challenges by streamlining the workflow to deliver valuable insights from massive quantities of data across multiple platforms, environments and locations. BigQuery Querying massive datasets can be time consuming and expensive without the right hardware and infrastructure. Google BigQuery solves this problem by enabling super-fast, SQL-like queries against append-only tables, using the processing power of Google’s infrastructure. Simply move your data into BigQuery and let us handle the hard work. You can control access to both the project and your data based on your business needs, such as giving others the ability to view or query your data. You can access BigQuery by using a web UI or a command-line tool, or by making calls to the BigQuery REST API using a variety of client libraries such as Java, PHP or Python. There are also a variety of third-party tools that you can use to interact with BigQuery, such as visualizing the data or loading the data. Get started now with creating an app, running a web query or using the command-line tool, or read on for more information about BigQuery fundamentals and how you can work with the product. BigQuery Big Data Visualization With D3.js Binarized Back Propagation Binarized Deep Neural Network(BDNN) In this work we introduce a binarized deep neural network (BDNN) model. BDNNs are trained using a novel binarized back propagation algorithm (BBP), which uses binary weights and binary neurons during the forward and backward propagation, while retaining precision of the stored weights in which gradients are accumulated. At test phase, BDNNs are fully binarized and can be implemented in hardware with low circuit complexity. The proposed binarized networks can be implemented using binary convolutions and proxy matrix multiplications with only standard binary XNOR and population count (popcount) operations. BBP is expected to reduce energy consumption by at least two orders of magnitude when compared to the hardware implementation of existing training algorithms. We obtained near state-of-the-art results with BDNNs on the permutation-invariant MNIST, CIFAR-10 and SVHN datasets. BinaryNet We introduce BinaryNet, a method which trains DNNs with binary weights and activations when computing parameters’ gradient. We show that it is possible to train a Multi Layer Perceptron (MLP) on MNIST and ConvNets on CIFAR-10 and SVHN with BinaryNet and achieve nearly state-of-the-art results. At run-time, BinaryNet drastically reduces memory usage and replaces most multiplications by 1-bit exclusive-not-or (XNOR) operations, which might have a big impact on both general-purpose and dedicated Deep Learning hardware. We wrote a binary matrix multiplication GPU kernel with which it is possible to run our MNIST MLP 7 times faster than with an unoptimized GPU kernel, without suffering any loss in classification accuracy. The code for BinaryNet is available. Binning Data binning is a data pre-processing technique used to reduce the effects of minor observation errors. The original data values which fall in a given small interval, a bin, are replaced by a value representative of that interval, often the central value. It is a form of quantization. Binning is the term used in scoring modeling for what is also known in Machine Learning as Discretization, the process of transforming a continuous characteristic into a finite number of intervals (the bins), which allows for a better understanding of its distribution and its relationship with a binary variable. The bins generated by the this process will eventually become the attributes of a predictive characteristic, the key component of a Scorecard. http://…optimal-binning-for-scoring-modeling.html Binomial Options Pricing Model(BOPM) In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein in 1979. Essentially, the model uses a ‘discrete-time’ (lattice based) model of the varying price over time of the underlying financial instrument. In general, binomial options pricing models do not have closed-form solutions. (Binomial Tree Option Model) Bio7 The application Bio7 is an integrated development environment for ecological modelling and contains powerful tools for model creation, scientific image analysis and statistical analysis. The application itself is based on an RCP-Eclipse-Environment (Rich-Client-Platform) which offers a huge flexibility in configuration and extensibility because of its plug-in structure and the possibility of customization. Features: • Creation and analysis of simulation models. • Statistical analysis. • Advanced R Graphical User Interface with editor, spreadsheet, ImageJ plot device and debugging interface. • Spatial statistics (possibility to send values from a specialized panel to R). • Image Analysis (embedded ImageJ). • Fast transfer of image data from ImageJ to R and vice versa. • Fast communication between R and Java (with RServe) and the possibilty to use R methods inside Java. • Interpretation of Java and script creation (BeanShell, Groovy, Jython). • Dynamic compilation of Java. • Creation of methods for Java, BeanShell, Groovy, Jython and R (integrated editors for Java, R, BeanShell, Groovy, Jython). • Sensitivity analysis with an embedded flowchart editor in which scripts, macros and compiled code can be dragged and executed. • Creation of 3d OpenGL (Jogl) models. • Visualizations and simulations on an embedded 3d globe (World Wind Java SDK). • Creation of Graphical User Interfaces with the embedded JavaFX SceneBuilder. Bipartite Graph In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint sets U and V (that is, U and V are each independent sets) such that every edge connects a vertex in U to one in V. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles. Biplot Biplots are a type of exploratory graph used in statistics, a generalization of the simple two-variable scatterplot. A biplot allows information on both samples and variables of a data matrix to be displayed graphically. Samples are displayed as points while variables are displayed either as vectors, linear axes or nonlinear trajectories. In the case of categorical variables, category level points may be used to represent the levels of a categorical variable. A generalised biplot displays information on both continuous and categorical variables. BiSeg We present a simple and effective framework for simultaneous semantic segmentation and instance segmentation with Fully Convolutional Networks (FCNs). The method, called BiSeg, predicts instance segmentation as a posterior in Bayesian inference, where semantic segmentation is used as a prior. We extend the idea of position-sensitive score maps used in recent methods to a fusion of multiple score maps at different scales and partition modes, and adopt it as a robust likelihood for instance segmentation inference. As both Bayesian inference and map fusion are performed per pixel, BiSeg is a fully convolutional end-to-end solution that inherits all the advantages of FCNs. We demonstrate state-of-the-art instance segmentation accuracy on PASCAL VOC. Bitcoin Bitcoin is a payment system invented by Satoshi Nakamoto in 2008 and introduced as open-source software in 2009. The system is peer-to-peer; all nodes verify transactions in a public distributed ledger called the block chain. The ledger uses its own unit of account, also called bitcoin. The system works without a central repository or single administrator, which has led the US Treasury to categorize it as a decentralized virtual currency. While bitcoin is not the first virtual currency, it is the first decentralized digital currency and cryptocurrency. It is the largest of its kind in terms of total market value. blabr Scientific computing for the web. Create your own interactive computation directly in the browser. Share on the web. Black-Box Optimization Benchmarking(BBOB) Black-Litterman Model In finance, the Black-Litterman model is a mathematical model for portfolio allocation developed in 1990 at Goldman Sachs by Fischer Black and Robert Litterman, and published in 1992. It seeks to overcome problems that institutional investors have encountered in applying modern portfolio theory in practice. The model starts with the equilibrium assumption that the asset allocation of a representative agent should be proportional to the market values of the available assets, and then modifies that to take into account the ‘views’ (i.e., the specific opinions about asset returns) of the investor in question to arrive at a bespoke asset allocation. BlackOut We propose BlackOut, an approximation algorithm to efficiently train massive recurrent neural network language models (RNNLMs) with million word vocabularies. BlackOut is motivated by using a discriminative loss, and we describe a new sampling strategy which significantly reduces computation while improving stability, sample efficiency, and rate of convergence. One way to understand BlackOut is to view it as an extension of the DropOut strategy to the output layer, wherein we use a discriminative training loss and a weighted sampling scheme. We also establish close connections between BlackOut, importance sampling, and noise contrastive estimation (NCE). Our experiments, on the recently released one billion word language modeling benchmark, demonstrate scalability and accuracy of BlackOut; we outperform the state-of-the art, and achieve the lowest perplexity scores on this dataset. Moreover, unlike other established methods which typically require GPUs or CPU clusters, we show that a carefully implemented version of BlackOut requires only 1-10 days on a single machine to train a RNNLM with a million word vocabulary and billions of parameters on one billion of words. Bland-Altman Plot A Bland-Altman plot (Difference plot) in analytical chemistry and biostatistics is a method of data plotting used in analyzing the agreement between two different assays. It is identical to a Tukey mean-difference plot, the name by which it is known in other fields, but was popularised in medical statistics by J. Martin Bland and Douglas G. Altman. BlandAltmanLeh Bleach In this paper we address the problem of rule-based stream data cleaning, which sets stringent requirements on latency, rule dynamics and ability to cope with the unbounded nature of data streams. We design a system, called Bleach, which achieves real-time violation detection and data repair on a dirty data stream. Bleach relies on efficient, compact and distributed data structures to maintain the necessary state to repair data, using an incremental version of the equivalence class algorithm. Additionally, it supports rule dynamics and uses a ‘cumulative’ sliding window operation to improve cleaning accuracy. We evaluate a prototype of Bleach using a TPC-DS derived dirty data stream and observe its high throughput, low latency and high cleaning accuracy, even with rule dynamics. Experimental results indicate superior performance of Bleach compared to a baseline system built on the micro-batch streaming paradigm. Blinder-Oaxaca Decomposition The Blinder-Oaxaca decomposition technique, or simply the Oaxaca decomposition, decomposes wage differentials into two components: a portion that arises because two comparison groups, on average, have different qualifications or credentials (e.g., years of schooling and experience in the labor market) when both groups receive the same treatment (explained component), and a portion that arises because one group is more favorably treated than the other given the same individual characteristics (unexplained component). The two portions are also called characteristics and coefficients effect using the terminology of regression analysis, which provides the basis of this decomposition technique. The coefficients effect is frequently interpreted as a measure of labor market discrimination. For a comprehensive review of issues related to labor market discrimination, see Joseph Altonji and Rebecca Blank (1999). oaxaca Block Chain A block chain is a transaction database shared by all nodes participating in a system based on the Bitcoin protocol. A full copy of a currency’s block chain contains every transaction ever executed in the currency. With this information, one can find out how much value belonged to each address at any point in history. Every block contains a hash of the previous block. This has the effect of creating a chain of blocks from the genesis block to the current block. Each block is guaranteed to come after the previous block chronologically because the previous block’s hash would otherwise not be known. Each block is also computationally impractical to modify once it has been in the chain for a while because every block after it would also have to be regenerated. These properties are what make double-spending of bitcoins very difficult. The block chain is the main innovation of Bitcoin. The block chain is a public ledger that records bitcoin transactions. A novel solution accomplishes this without any trusted central authority: maintenance of the block chain is performed by a network of communicating nodes running bitcoin software. Transactions of the form payer X sends Y bitcoins to payee Z are broadcast to this network using readily available software applications. Network nodes can validate transactions, add them to their copy of the ledger, and then broadcast these ledger additions to other nodes. The block chain is a distributed database; in order to independently verify the chain of ownership of any and every bitcoin (amount), each network node stores its own copy of the block chain. Approximately six times per hour, a new group of accepted transactions, a block, is created, added to the block chain, and quickly published to all nodes. This allows bitcoin software to determine when a particular bitcoin amount has been spent, which is necessary in order to prevent double-spending in an environment without central oversight. Whereas a conventional ledger records the transfers of actual bills or promissory notes that exist apart from it, the block chain is the only place that bitcoins can be said to exist in the form of unspent outputs of transactions. Blockchain Technology Explained Block Power Methods This paper is concerned with the extension of the power method, used for finding the largest eigenvalue and associated eigenvector of a matrix, to its block from for computing the largest block eigenvalue and associated block eigenvector of a non-symmetric matrix. Based on the developed block power method, several algorithms are developed for solving the complete set of solvents and spectral factors of a matrix polynomial, without prior knowledge of the latent roots of the matrix polynomial. Moreover, when any right/left solvent of a matrix polynomial is given, the proposed method can be used to determine the corresponding left/right solvent such that both right and left solvents have the same eigenspectra. The matrix polynomial of interest must have distinct block solvents and a corresponding non-singular polynomial matrix. The established algorithms can be applied in the analysis and/or design of systems described by high-degree vector differential equations and/or matrix fraction descriptions. Blockspring Blockspring lets you dramatically scale analytics with limited technical resources. It’s a platform that makes distribution and consumption of technology simple within your organization. Here’s how it works: • Developers and data scientists post common company functions – queries, algorithms, visualizations, API calls, etc – to Blockspring in their favorite programming language. • Business users search Blockspring for the function they need, and easily use it in their spreadsheet. This model helps IT teams produced more functionality. Simultaneously, it lets business users find and use the tools they need, when they need them. Bloom Filter A Bloom filter is a space-efficient probabilistic data structure, conceived by Burton Howard Bloom in 1970, that is used to test whether an element is a member of a set. False positive matches are possible, but false negatives are not, thus a Bloom filter has a 100% recall rate. In other words, a query returns either “possibly in set” or “definitely not in set”. Elements can be added to the set, but not removed (though this can be addressed with a “counting” filter). The more elements that are added to the set, the larger the probability of false positives. Bloom proposed the technique for applications where the amount of source data would require an impracticably large hash area in memory if “conventional” error-free hashing techniques were applied. He gave the example of a hyphenation algorithm for a dictionary of 500,000 words, out of which 90% follow simple hyphenation rules, but the remaining 10% require expensive disk accesses to retrieve specific hyphenation patterns. With sufficient core memory, an error-free hash could be used to eliminate all unnecessary disk accesses; on the other hand, with limited core memory, Bloom’s technique uses a smaller hash area but still eliminates most unnecessary accesses. For example, a hash area only 15% of the size needed by an ideal error-free hash still eliminates 85% of the disk accesses (Bloom (1970)). Blossom Belief Propagation(Blossom-BP) Max-product Belief Propagation (BP) is a popular message-passing algorithm for computing a Maximum-A-Posteriori (MAP) assignment over a distribution represented by a Graphical Model (GM). It has been shown that BP can solve a number of combinatorial optimization problems including minimum weight matching, shortest path, network flow and vertex cover under the following common assumption: the respective Linear Programming (LP) relaxation is tight, i.e., no integrality gap is present. However, when LP shows an integrality gap, no model has been known which can be solved systematically via sequential applications of BP. In this paper, we develop the first such algorithm, coined Blossom-BP, for solving the minimum weight matching problem over arbitrary graphs. Each step of the sequential algorithm requires applying BP over a modified graph constructed by contractions and expansions of blossoms, i.e., odd sets of vertices. Our scheme guarantees termination in O(n^2) of BP runs, where n is the number of vertices in the original graph. In essence, the Blossom-BP offers a distributed version of the celebrated Edmonds’ Blossom algorithm by jumping at once over many sub-steps with a single BP. Moreover, our result provides an interpretation of the Edmonds’ algorithm as a sequence of LPs. BlueSky Statistics Fully featured Statistics application and development framework built on the open source R project. Provides familiar powerful user interface available in mainstream statistical applications like SPSS, SAS etc. Unlocks the power of R for the analyst community by providing a rich GUI and output for several popular statistics, data mining, data manipulation and graphics commands, all out of the box… Provide a rich development framework for developing and deploying new statistical modules, applications or functions with rich graphical user interfaces and output, all through intuitive drag and drop user interfaces (No programming required). A quick look at BlueSky Statistics Bokeh Bokeh is a Python interactive visualization library that targets modern web browsers for presentation. Its goal is to provide elegant, concise construction of novel graphics in the style of D3.js, but also deliver this capability with high-performance interactivity over very large or streaming datasets. Bokeh can help anyone who would like to quickly and easily create interactive plots, dashboards, and data applications. bolt Bringing multi-dimensional arrays to distributed settings through a unified Python interface. Bolt is an open source library providing a Python interface to ndarrays backed by local or distributed implementations (currently targeting Spark). We want to make working with big array data in Python as easy and seamless as in local settings, while exploiting the speed of proven distributed engines. Boosting Boosting is a machine learning meta-algorithm for reducing bias in supervised learning. Boosting is based on the question posed by Kearns: Can a set of weak learners create a single strong learner? A weak learner is defined to be a classifier which is only slightly correlated with the true classification (it can label examples better than random guessing). In contrast, a strong learner is a classifier that is arbitrarily well-correlated with the true classification. Schapire’s affirmative answer to Kearns’ question has had significant ramifications in machine learning and statistics, most notably leading to the development of boosting. Bootstrap Aggregating(Bagging) Bootstrap aggregating, also called bagging, is a machine learning ensemble meta-algorithm designed to improve the stability and accuracy of machine learning algorithms used in statistical classification and regression. It also reduces variance and helps to avoid overfitting. Although it is usually applied to decision tree methods, it can be used with any type of method. Bagging is a special case of the model averaging approach. Bootstrap Lasso + Partial Ridge(LPR) For high-dimensional sparse linear models, how to construct confidence intervals for coefficients remains a difficult question. The main reason is the complicated limiting distributions of common estimators such as the Lasso. Several confidence interval construction methods have been developed, and Bootstrap Lasso+OLS is notable for its simple technicality, good interpretability, and comparable performance with other more complicated methods. However, Bootstrap Lasso+OLS depends on the beta-min assumption, a theoretic criterion that is often violated in practice. In this paper, we introduce a new method called Bootstrap Lasso+Partial Ridge (LPR) to relax this assumption. LPR is a two-stage estimator: first using Lasso to select features and subsequently using Partial Ridge to refit the coefficients. Simulation results show that Bootstrap LPR outperforms Bootstrap Lasso+OLS when there exist small but non-zero coefficients, a common situation violating the beta-min assumption. For such coefficients, compared to Bootstrap Lasso+OLS, confidence intervals constructed by Bootstrap LPR have on average 50% larger coverage probabilities. Bootstrap LPR also has on average 35% shorter confidence interval lengths than the de-sparsified Lasso methods, regardless of whether linear models are misspecified. Additionally, we provide theoretical guarantees of Bootstrap LPR under appropriate conditions and implement it in the R package ‘HDCI.’ Bootstrap Percolation The name percolation probably relates for most people to brewing coffee, where the water fumes go throw the coffee powder. This example is only one of many systems in which perculation phenomenon exists.To understand it a bit more, one can think of a mixture of glass and metal balls in a jar. up to a certain precentage of metal balls the mixture would behave as an insulator, that is there would be no group of metal balls touching each other that would reach from one side of the jar to the other. From a certain precentage called the percolation threshhold Pc such a group would exist and the mixture would behave as a conductor.The percolation threshold is defined as the probability below which no infinite cluster is found in the infinite system. A group of touching metal balls is named a cluster and the group that reaches from one end to the other is called the spanning cluster. Bootstrap-Enhanced Least Absolute Shrinkage Operator(Bolasso) Using the bootstrap and intersecting the supports, we actually get a consistent model estimate, without the consistency condition required by the regular Lasso. We refer to this new procedure as the Bolasso (bootstrap-enhanced least absolute shrinkage operator). Finally, our Bolasso framework could be seen as a voting scheme applied to the supports of the bootstrap Lasso estimates; however, our procedure may rather be considered as a consensus combination scheme, as we keep the (largest) subset of variables on which all regressors agree in terms of variable selection, which is in our case provably consistent and also allows to get rid of a potential additional hyperparameter. Bootstrapping In statistics, bootstrapping is a method for assigning measures of accuracy (defined in terms of bias, variance, confidence intervals, prediction error or some other such measure) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using only very simple methods. Generally, it falls in the broader class of resampling methods. Border-Peeling Clustering In this paper, we present a novel non-parametric clustering technique, which is based on an iterative algorithm that peels off layers of points around the clusters. Our technique is based on the notion that each latent cluster is comprised of layers that surround its core, where the external layers, or border points, implicitly separate the clusters. Analyzing the K-nearest neighbors of the points makes it possible to identify the border points and associate them with points of inner layers. Our clustering algorithm iteratively identifies border points, peels them, and separates the latent clusters. We show that the peeling process adapts to the local density and successfully separates adjacent clusters. A notable quality of the Border-Peeling algorithm is that it does not require any parameter tuning in order to outperform state-of-the-art finely-tuned non-parametric clustering methods, including Mean-Shift and DBSCAN. We further assess our technique on high-dimensional datasets that vary in size and characteristics. In particular, we analyze the space of deep features that were trained by a convolutional neural network. Borealis A generalized global update algorithm for Boolean optimization problems. Optimization problems with Boolean variables that fall into the nondeterministic polynomial (NP) class are of fundamental importance in computer science, mathematics, physics and industrial applications. Most notably, solving constraint-satisfaction problems, which are related to spin-glass-like Hamiltonians in physics, remains a difficult numerical task. As such, there has been great interest in designing efficient heuristics to solve these computationally difficult problems. Inspired by parallel tempering Monte Carlo in conjunction with the rejection-free isoenergetic cluster algorithm developed for Ising spin glasses, we present a generalized global update optimization heuristic that can be applied to different NP-complete problems with Boolean variables. The global cluster updates allow for a wide-spread sampling of phase space, thus considerably speeding up optimization. By carefully tuning the pseudo-temperature (needed to randomize the configurations) of the problem, we show that the method can efficiently tackle optimization problems with over-constraints or on topologies with a large site-percolation threshold. We illustrate the efficiency of the heuristic on paradigmatic optimization problems, such as the maximum satisfiability problem and the vertex cover problem. Boruta Machine learning methods are often used to classify objects described by hundreds of attributes; in many applications of this kind a great fraction of attributes may be totally irrelevant to the classification problem. Even more, usually one cannot decide a priori which attributes are relevant. In this paper we present an improved version of the algorithm for identification of the full set of truly important variables in an information system. It is an extension of the random forest method which utilises the importance measure generated by the original algorithm. It compares, in the iterative fashion, the importances of original attributes with importances of their randomised copies. We analyse performance of the algorithm on several examples of synthetic data, as well as on a biologically important problem, namely on identification of the sequence motifs that are important for aptameric activity of short RNA sequences. Boruta Bowtie Bowtie is a library for writing dashboards in Python. No need to know web frameworks or JavaScript, focus on building functionality in Python. Interactively explore your data in new ways! Deploy and share with others! Box–Muller Transform The Box-Muller transform (by George Edward Pelham Box and Mervin Edgar Muller 1958) is a pseudo-random number sampling method for generating pairs of independent, standard, normally distributed (zero expectation, unit variance) random numbers, given a source of uniformly distributed random numbers. It is commonly expressed in two forms. The basic form as given by Box and Muller takes two samples from the uniform distribution on the interval (0, 1] and maps them to two standard, normally distributed samples. The polar form takes two samples from a different interval, [-1, +1], and maps them to two normally distributed samples without the use of sine or cosine functions. The Box-Muller transform was developed as a more computationally efficient alternative to the inverse transform sampling method. The Ziggurat algorithm gives an even more efficient method. Boxplot In descriptive statistics, a box plot or boxplot is a convenient way of graphically depicting groups of numerical data through their quartiles. Box plots may also have lines extending vertically from the boxes (whiskers) indicating variability outside the upper and lower quartiles, hence the terms box-and-whisker plot and box-and-whisker diagram. Outliers may be plotted as individual points. Breadth-first Search(BFS) In graph theory, breadth-first search (BFS) is a strategy for searching in a graph when search is limited to essentially two operations: (a) visit and inspect a node of a graph; (b) gain access to visit the nodes that neighbor the currently visited node. The BFS begins at a root node and inspects all the neighboring nodes. Then for each of those neighbor nodes in turn, it inspects their neighbor nodes which were unvisited, and so on. Compare BFS with the equivalent, but more memory-efficient Iterative deepening depth-first search and contrast with depth-first search. Breakout A breakout is typically characterized by two steady states and an intermediate transition period. Broadly speaking, breakouts have two flavors: 1. Mean shift: A sudden jump in the time series corresponds to a mean shift. A sudden jump in CPU utilization from 40% to 60% would exemplify a mean shift. 2. Ramp up: A gradual increase in the value of the metric from one steady state to another constitutes a ramp up. A gradual increase in CPU utilization from 40% to 60% would exemplify a ramp up. Bridge Sampling (Bennett, 1976; Meng & Wong, 1996), a reliable and relatively straightforward sampling method that allows researchers to obtain the marginal likelihood for models of varying complexity. Broyden–Fletcher–Goldfarb–Shanno Algorithm(BFGS) In numerical optimization, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems. The BFGS method approximates Newton’s method, a class of hill-climbing optimization techniques that seeks a stationary point of a (preferably twice continuously differentiable) function. For such problems, a necessary condition for optimality is that the gradient be zero. Newton’s method and the BFGS methods are not guaranteed to converge unless the function has a quadratic Taylor expansion near an optimum. These methods use both the first and second derivatives of the function. However, BFGS has proven to have good performance even for non-smooth optimizations. BUbiNG BUbiNG is an opensource Java fully distributed crawler; a single BUbiNG agent, using sizeable hardware, can crawl several thousands pages per second respecting strict politeness constraints, both host- and IP-based. Unlike existing open-source distributed crawlers that rely on batch techniques (like MapReduce), BUbiNG job distribution is based on modern high-speed protocols so to achieve very high throughput. Bucketization Bumping Bumping is a simple algorithm that can help your classifier escape from a local minimum. The idea behind bumping is that we can break the symmetry of the problem (or escape the local minimum) by training a decision tree on random subsample. This is similar to bagging. The hope is that in the subsample there will be a preferred split so the tree can pick it. We fit several trees on different bootstrap) samples (sampling with replacement) and choose the one with the best performance on the full training set as the winner. The more rounds of bumping we do, the more likely we are to escape. It costs more CPU time as well though. Bumps Chart Bump charts got their name from ‘bumps race’, a term used to refer to a boat race where each boat tries to ‘bump’ the one in front and move up the chart. Bump charts have become quite common of late and are typically used to represent changes in the position of a given number of competing entities over a fixed time duration. Burning Number We introduce a new graph parameter called the burning number, inspired by contact processes on graphs such as graph bootstrap percolation, and graph searching paradigms such as Firefighter. The burning number measures the speed of the spread of contagion in a graph; the lower the burning number, the faster the contagion spreads. We provide a number of properties of the burning number, including characterizations and bounds. The burning number is computed for several graph classes, and is derived for the graphs generated by the Iterated Local Transitivity model for social networks. Business Analysis Body of Knowledge(BABOK) A Guide to the Business Analysis Body of Knowledge (BABOK) is the written guide to the collection of business analysis knowledge reflecting current best practice, providing a framework that describes the areas of knowledge, with associated activities and tasks and techniques required. According to Capability Maturity Model Integration, organisations interested in process improvement need to adopt industry standards from the Business Analysis Body of Knowledge (and other associated references) to lift their project delivery from the ad hoc to the managed level. Business Analytics Business analytics (BA) refers to the skills, technologies, applications and practices for continuous iterative exploration and investigation of past business performance to gain insight and drive business planning. Business analytics focuses on developing new insights and understanding of business performance based on data and statistical methods. In contrast, business intelligence traditionally focuses on using a consistent set of metrics to both measure past performance and guide business planning, which is also based on data and statistical methods. Business Function Library(BFL) The Business Function Library (BFL) is one of the SAP AFL (Application Function) Libraries. It contains pre-built parameter-driven functions in the financial area. The functions are implemented by C++. This library helps you develop compound business algorithms that are fully compliant with the SAP HANA calculation engine. It offers you the flexibility and efficiency to develop HANA-based applications with incredible performance. Business Intelligence(BI) Business intelligence (BI) is a set of theories, methodologies, architectures, and technologies that transform raw data into meaningful and useful information for business purposes. BI can handle enormous amounts of unstructured data to help identify, develop and otherwise create new opportunities. BI, in simple words, makes interpreting voluminous data friendly. Making use of new opportunities and implementing an effective strategy can provide a competitive market advantage and long-term stability. Business Intelligence Competency Centers(BICC) A Business Intelligence Competency Center (BICC) is a cross-functional organizational team that has defined tasks, roles, responsibilities and processes for supporting and promoting the effective use of Business Intelligence (BI) across an organization. As early as 2001, Gartner, an information technology research and advisory company, started advocating that companies need a BICC to develop and focus resources to be successful using business intelligence. Since then, the BICC concept has been further refined through practical implementations in organizations that have implemented BI and analytical software. In practice, the term ‘BICC’ is not well integrated into the nomenclature of business or public sector organizations and there are a large degree of variances in the organizational design for BICCs. Nevertheless, the popularity of the BICC concept has caused the creation of units that focus on ensuring the use of the information for decision-making from BI software and increasing the return on investment (ROI) of BI. A BICC coordinates the activities and resources to ensure that a fact-based approach to decision making is systematically implemented throughout an organization. It has responsibility for the governance structure for BI and analytical programs, projects, practices, software, and architecture. It is responsible for building the plans, priorities, infrastructure, and competencies that the organization needs to take forward-looking strategic decisions by using the BI and analytical software capabilities. A BICC’s influence transcends that of a typical business unit, playing a crucial central role in the organizational change and strategic process. Accordingly, the BICC’s purpose is to empower the entire organization to coordinate BI from all units. Through centralization, it ‘…ensures that information and best practices are communicated and shared through the entire organization so that everyone can benefit from successes and lessons learned.’ The BICC also plays an important organizational role facilitating interaction among the various cultures and units within the organization. Knowledge transfer, enhancement of analytic skills, coaching and training are central to the mandate of the BICC. A BICC should be pivotal in ensuring a high degree of information consumption and a ROI for BI. Byzantine Gradient Descent We consider the problem of distributed statistical machine learning in adversarial settings, where some unknown and time-varying subset of working machines may be compromised and behave arbitrarily to prevent an accurate model from being learned. This setting captures the potential adversarial attacks faced by Federated Learning — a modern machine learning paradigm that is proposed by Google researchers and has been intensively studied for ensuring user privacy. Formally, we focus on a distributed system consisting of a parameter server and $m$ working machines. Each working machine keeps $N/m$ data samples, where $N$ is the total number of samples. The goal is to collectively learn the underlying true model parameter of dimension $d$. In classical batch gradient descent methods, the gradients reported to the server by the working machines are aggregated via simple averaging, which is vulnerable to a single Byzantine failure. In this paper, we propose a Byzantine gradient descent method based on the geometric median of means of the gradients. We show that our method can tolerate $q \le (m-1)/2$ Byzantine failures, and the parameter estimate converges in $O(\log N)$ rounds with an estimation error of $\sqrt{d(2q+1)/N}$, hence approaching the optimal error rate $\sqrt{d/N}$ in the centralized and failure-free setting. The total computational complexity of our algorithm is of $O((Nd/m) \log N)$ at each working machine and $O(md + kd \log^3 N)$ at the central server, and the total communication cost is of $O(m d \log N)$. We further provide an application of our general results to the linear regression problem. A key challenge arises in the above problem is that Byzantine failures create arbitrary and unspecified dependency among the iterations and the aggregated gradients. We prove that the aggregated gradient converges uniformly to the true gradient function.