W2VLDA With the increase of online customer opinions in specialised websites and social networks, the necessity of automatic systems to help to organise and classify customer reviews by domain-specific aspect/categories and sentiment polarity is more important than ever. Supervised approaches to Aspect Based Sentiment Analysis obtain good results for the domain/language their are trained on, but having manually labelled data for training supervised systems for all domains and languages use to be very costly and time consuming. In this work we describe W2VLDA, an unsupervised system based on topic modelling, that combined with some other unsupervised methods and a minimal configuration, performs aspect/category classifiation, aspectterms/opinion-words separation and sentiment polarity classification for any given domain and language. We also evaluate the performance of the aspect and sentiment classification in the multilingual SemEval 2016 task 5 (ABSA) dataset. We show competitive results for several languages (English, Spanish, French and Dutch) and domains (hotels, restaurants, electronic-devices).
Waffle Chart / Square Pie Chart A little-known alternative to the round pie chart is the square pie or waffle chart. It consists of a square that is divided into 10×10 cells, making it possible to read values precisely down to a single percent. Depending on how the areas are laid out (as square as possible seems to be the best idea), it is very easy to compare parts to the whole.
Waikato Environment for Knowledge Analysis
Weka (Waikato Environment for Knowledge Analysis) is a popular suite of machine learning software written in Java, developed at the University of Waikato, New Zealand. Weka is free software available under the GNU General Public License.
wakefield wakefield is a Github based R package which is designed to quickly generate random data sets. The user passes n (number of rows) and predefined vectors to the r_data_frame function to produce a dplyr::tbl_df object.
Wake-Sleep Algorithm The wake-sleep algorithm is an unsupervised learning algorithm for a multilayer neural network (e.g. sigmoid belief net). Training is divided into two phases, ‘wake’ and ‘sleep’. In the ‘wake’ phase, neurons are driven by recognition connections (connections from what would normally be considered an input to what is normally considered an output), while generative connections (those from outputs to inputs) are modified to increase the probability that they would reconstruct the correct activity in the layer below (closer to the sensory input). In the ‘sleep’ phase the process is reversed: neurons are driven by generative connections, while recognition connections are modified to increase the probability that they would produce the correct activity in the layer above (further from sensory input).
Walktrap Community Algorithm Tries to find densely connected subgraphs, also called communities in a graph via random walks. The idea is that short random walks tend to stay in the same community.
Walsh Figure of Merit LowWAFOMNX
Ward Hierarchical Clustering “Ward’s Method”
Ward’s Hierarchical Clustering Method: Clustering Criterion and Agglomerative Algorithm
Ward’s Method In statistics, Ward’s method is a criterion applied in hierarchical cluster analysis. Ward’s minimum variance method is a special case of the objective function approach originally presented by Joe H. Ward, Jr. Ward suggested a general agglomerative hierarchical clustering procedure, where the criterion for choosing the pair of clusters to merge at each step is based on the optimal value of an objective function. This objective function could be ‘any function that reflects the investigator’s purpose.’ Many of the standard clustering procedures are contained in this very general class. To illustrate the procedure, Ward used the example where the objective function is the error sum of squares, and this example is known as Ward’s method or more precisely Ward’s minimum variance method.
Ward’s Method
WarpLDA Developing efficient and scalable algorithms for Latent Dirichlet Allocation (LDA) is of wide interest for many applications. Previous work has developed an $O(1)$ Metropolis-Hastings sampling method for each token. However, the performance is far from being optimal due to random accesses to the parameter matrices and frequent cache misses. In this paper, we propose WarpLDA, a novel $O(1)$ sampling algorithm for LDA. WarpLDA is a Metropolis-Hastings based algorithm which is designed to optimize the cache hit rate. Advantages of WarpLDA include 1) Efficiency and scalability: WarpLDA has good locality and carefully designed partition method, and can be scaled to hundreds of machines; 2) Simplicity: WarpLDA does not have any complicated modules such as alias tables, hybrid data structures, or parameter servers, making it easy to understand and implement; 3) Robustness: WarpLDA is consistently faster than other algorithms, under various settings from small-scale to massive-scale dataset and model. WarpLDA is 5-15x faster than state-of-the-art LDA samplers, implying less cost of time and money. With WarpLDA users can learn up to one million topics from hundreds of millions of documents in a few hours, at the speed of 2G tokens per second, or learn topics from small-scale datasets in seconds.
Wasserstein Auto-Encoder
We propose the Wasserstein Auto-Encoder (WAE)—a new algorithm for building a generative model of the data distribution. WAE minimizes a penalized form of the Wasserstein distance between the model distribution and the target distribution, which leads to a different regularizer than the one used by the Variational Auto-Encoder (VAE). This regularizer encourages the encoded training distribution to match the prior. We compare our algorithm with several other techniques and show that it is a generalization of adversarial auto-encoders (AAE). Our experiments show that WAE shares many of the properties of VAEs (stable training, encoder-decoder architecture, nice latent manifold structure) while generating samples of better quality, as measured by the FID score.
Wasserstein CNN
Heterogeneous face recognition (HFR) aims to match facial images acquired from different sensing modalities with mission-critical applications in forensics, security and commercial sectors. However, HFR is a much more challenging problem than traditional face recognition because of large intra-class variations of heterogeneous face images and limited training samples of cross-modality face image pairs. This paper proposes a novel approach namely Wasserstein CNN (convolutional neural networks, or WCNN for short) to learn invariant features between near-infrared and visual face images (i.e. NIR-VIS face recognition). The low-level layers of WCNN are trained with widely available face images in visual spectrum. The high-level layer is divided into three parts, i.e., NIR layer, VIS layer and NIR-VIS shared layer. The first two layers aims to learn modality-specific features and NIR-VIS shared layer is designed to learn modality-invariant feature subspace. Wasserstein distance is introduced into NIR-VIS shared layer to measure the dissimilarity between heterogeneous feature distributions. So W-CNN learning aims to achieve the minimization of Wasserstein distance between NIR distribution and VIS distribution for invariant deep feature representation of heterogeneous face images. To avoid the over-fitting problem on small-scale heterogeneous face data, a correlation prior is introduced on the fully-connected layers of WCNN network to reduce parameter space. This prior is implemented by a low-rank constraint in an end-to-end network. The joint formulation leads to an alternating minimization for deep feature representation at training stage and an efficient computation for heterogeneous data at testing stage. Extensive experiments on three challenging NIR-VIS face recognition databases demonstrate the significant superiority of Wasserstein CNN over state-of-the-art methods.
Wasserstein Discriminant Analysis
Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear Discriminant Analysis (LDA), WDA selects the projection matrix that maximizes the ratio of two quantities: the dispersion of projected points coming from different classes, divided by the dispersion of projected points coming from the same class. To quantify dispersion, WDA uses regularized Wasserstein distances, rather than cross-variance measures which have been usually considered, notably in LDA. Thanks to the the underlying principles of optimal transport, WDA is able to capture both global (at distribution scale) and local (at samples scale) interactions between classes. Regularized Wasserstein distances can be computed using the Sinkhorn matrix scaling algorithm; We show that the optimization of WDA can be tackled using automatic differentiation of Sinkhorn iterations. Numerical experiments show promising results both in terms of prediction and visualization on toy examples and real life datasets such as MNIST and on deep features obtained from a subset of the Caltech dataset.
Wasserstein Distance “Wasserstein Metric”
Wasserstein GAN
We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore, we show that the corresponding optimization problem is sound, and provide extensive theoretical work highlighting the deep connections to other distances between distributions.
Wasserstein Identity Testing Problem Uniformity testing and the more general identity testing are well studied problems in distributional property testing. Most previous work focuses on testing under $L_1$-distance. However, when the support is very large or even continuous, testing under $L_1$-distance may require a huge (even infinite) number of samples. Motivated by such issues, we consider the identity testing in Wasserstein distance (a.k.a. transportation distance and earthmover distance) on a metric space (discrete or continuous). In this paper, we propose the Wasserstein identity testing problem (Identity Testing in Wasserstein distance). We obtain nearly optimal worst-case sample complexity for the problem. Moreover, for a large class of probability distributions satisfying the so-called ‘Doubling Condition’, we provide nearly instance-optimal sample complexity.
Wasserstein Introspective Neural Network
We present Wasserstein introspective neural networks (WINN) that are both a generator and a discriminator within a single model. WINN provides a significant improvement over the recent introspective neural networks (INN) method by enhancing INN’s generative modeling capability. WINN has three interesting properties: (1) A mathematical connection between the formulation of Wasserstein generative adversarial networks (WGAN) and the INN algorithm is made; (2) The explicit adoption of the WGAN term into INN results in a large enhancement to INN, achieving compelling results even with a single classifier on e.g., providing a 20 times reduction in model size over INN within texture modeling; (3) When applied to supervised classification, WINN also gives rise to greater robustness with an $88\%$ reduction of errors against adversarial examples — improved over the result of $39\%$ by an INN-family algorithm. In the experiments, we report encouraging results on unsupervised learning problems including texture, face, and object modeling, as well as a supervised classification task against adversarial attack.
Wasserstein Metric In mathematics, the Wasserstein (or Vasershtein) metric is a distance function defined between probability distributions on a given metric space M. Intuitively, if each distribution is viewed as a unit amount of ‘dirt’ piled on M, the metric is the minimum ‘cost’ of turning one pile into the other, which is assumed to be the amount of dirt that needs to be moved times the distance it has to be moved. Because of this analogy, the metric is known in computer science as the earth mover’s distance. The name ‘Wasserstein distance’ was coined by R. L. Dobrushin in 1970, after the Russian mathematician Leonid Vaseršteĭn who introduced the concept in 1969. Most English-language publications use the German spelling ‘Wasserstein’ (attributed to the name ‘Vasershtein’ being of German origin).
“Earth Mover’s Distance”
Wasserstein Distance
Watanabe-Akaike Information Criteria
WAIC (the Watanabe-Akaike or widely applicable information criterion; Watanabe, 2010) can be viewed as an improvement on the deviance information criterion (DIC) for Bayesian models. DIC has gained popularity in recent years in part through its implementation in the graphical modeling package BUGS (Spiegelhalter, Best, et al., 2002; Spiegelhalter, Thomas, et al., 1994, 2003), but is known to have some problems, arising in part from it not being fully Bayesian in that it is based on a point estimate (van der Linde, 2005, Plummer, 2008). For example, DIC can produce negative estimates of the effective number of parameters in a model and it is not defined for singular models. WAIC is fully Bayesian and closely approximates Bayesian cross-validation. Unlike DIC, WAIC is invariant to parametrization and also works for singular models.
A Widely Applicable Bayesian Information Criterion
Waterfall Chart A waterfall chart is a form of data visualization that helps in understanding the cumulative effect of sequentially introduced positive or negative values. The waterfall chart is also known as a flying bricks chart or Mario chart due to the apparent suspension of columns (bricks) in mid-air. Often in finance, it will be referred to as a bridge. Waterfall charts were popularized by the strategic consulting firm McKinsey & Company in its presentations to clients. The waterfall chart is normally used for understanding how an initial value is affected by a series of intermediate positive or negative values. Usually the initial and the final values are represented by whole columns, while the intermediate values are denoted by floating columns. The columns are color-coded for distinguishing between positive and negative values.
“Waterfall Chart”
Understanding Waterfall Plots
Waterfall plots – what and how?
Waterfall Plot A waterfall plot is a three-dimensional plot in which multiple curves of data, typically spectra, are displayed simultaneously. Typically the curves are staggered both across the screen and vertically, with ‘nearer’ curves masking the ones behind. The result is a series of ‘mountain’ shapes that appear to be side by side. The waterfall plot is often used to show how two-dimensional information changes over time or some other variable such as rpm. The term ‘waterfall plot’ is sometimes used interchangeably with ‘spectrogram’ or ‘Cumulative Spectral Decay’ (CSD) plot.
Wavelet-like Auto-Encoder
Accelerating deep neural networks (DNNs) has been attracting increasing attention as it can benefit a wide range of applications, e.g., enabling mobile systems with limited computing resources to own powerful visual recognition ability. A practical strategy to this goal usually relies on a two-stage process: operating on the trained DNNs (e.g., approximating the convolutional filters with tensor decomposition) and fine-tuning the amended network, leading to difficulty in balancing the trade-off between acceleration and maintaining recognition performance. In this work, aiming at a general and comprehensive way for neural network acceleration, we develop a Wavelet-like Auto-Encoder (WAE) that decomposes the original input image into two low-resolution channels (sub-images) and incorporate the WAE into the classification neural networks for joint training. The two decomposed channels, in particular, are encoded to carry the low-frequency information (e.g., image profiles) and high-frequency (e.g., image details or noises), respectively, and enable reconstructing the original input image through the decoding process. Then, we feed the low-frequency channel into a standard classification network such as VGG or ResNet and employ a very lightweight network to fuse with the high-frequency channel to obtain the classification result. Compared to existing DNN acceleration solutions, our framework has the following advantages: i) it is tolerant to any existing convolutional neural networks for classification without amending their structures; ii) the WAE provides an interpretable way to preserve the main components of the input image for classification.
WaveNet This paper introduces WaveNet, a deep neural network for generating raw audio waveforms. The model is fully probabilistic and autoregressive, with the predictive distribution for each audio sample conditioned on all previous ones; nonetheless we show that it can be efficiently trained on data with tens of thousands of samples per second of audio. When applied to text-to-speech, it yields state-of-the-art performance, with human listeners rating it as significantly more natural sounding than the best parametric and concatenative systems for both English and Mandarin. A single WaveNet can capture the characteristics of many different speakers with equal fidelity, and can switch between them by conditioning on the speaker identity. When trained to model music, we find that it generates novel and often highly realistic musical fragments. We also show that it can be employed as a discriminative model, returning promising results for phoneme recognition.
W-Decorrelation Estimators computed from adaptively collected data do not behave like their non-adaptive brethren. Rather, the sequential dependence of the collection policy can lead to severe distributional biases that persist even in the infinite data limit. We develop a general method decorrelation procedure — W-decorrelation — for transforming the bias of adaptive linear regression estimators into variance. The method uses only coarse-grained information about the data collection policy and does not need access to propensity scores or exact knowledge of the policy. We bound the finite-sample bias and variance of the W-estimator and develop asymptotically correct confidence intervals based on a novel martingale central limit theorem. We then demonstrate the empirical benefits of the generic W-decorrelation procedure in two different adaptive data settings: the multi-armed bandits and autoregressive time series models.
Weakly Structured Information Processing and Exploration
WIPE is used for managing the graph traversal manipulation with BI-like data aggregation. WIPE stands for “Weakly-structured Information Processing and Exploration”. It is a data manipulation and query language built on top of the graph functionality in the SAP HANA Database. Like other domain specific languages provided by SAP HANA Database, WIPE is embedded in transactional context, which means that multiple WIPE statements can be executed concurrently, guaranteeing the atomicity, consistency, isolation and durability. With the help of this language, multiple graph operations such as inserting, updating or deleting a node and other query operations can be declared in one complex statement. It is the graph abstraction layer in the SAP HANA Database that provides interaction with the graph data stored in the database by exposing graph concepts directly to the application developer. The application developer can create or delete graphs, access the existing graphs, modify the vertices and edges of the graphs, or retrieve a set of vertices and edges based on their attributes. Besides retrieval and manipulation functions, a set of built-in graph operators are also provided by the SAP HANA Database. These operators, such as breadth-first or depth-first traversal algorithms, interact with the column store of the relational engine to execute efficiently and in a highly optimum manner.
Weaver We introduce a new distributed graph store, called Weaver, which enables efficient, transactional graph analyses as well as strictly serializable read-write transactions on dynamic graphs. The key insight that enables Weaver to combine strict serializability with horizontal scalability and high performance is a novel request ordering mechanism called refinable timestamps. This technique couples coarse-grained vector timestamps with a fine-grained timeline oracle to pay the overhead of strong consistency only when needed.
Web Analytics Web analytics is the measurement, collection, analysis and reporting of web data for purposes of understanding and optimizing web usage. Web analytics is not just a tool for measuring web traffic but can be used as a tool for business and market research, and to assess and improve the effectiveness of a website. Web analytics applications can also help companies measure the results of traditional print or broadcast advertising campaigns. It helps one to estimate how traffic to a website changes after the launch of a new advertising campaign. Web analytics provides information about the number of visitors to a website and the number of page views. It helps gauge traffic and popularity trends which is useful for market research. There are two categories of web analytics; off-site and on-site web analytics. Off-site web analytics refers to web measurement and analysis regardless of whether you own or maintain a website. It includes the measurement of a website’s potential audience (opportunity), share of voice (visibility), and buzz (comments) that is happening on the Internet as a whole. On-site web analytics measure a visitor’s behavior once on your website. This includes its drivers and conversions; for example, the degree to which different landing pages are associated with online purchases. On-site web analytics measures the performance of your website in a commercial context. This data is typically compared against key performance indicators for performance, and used to improve a website or marketing campaign’s audience response. Google Analytics is the most widely used on-site web analytics service; although new tools are emerging that provide additional layers of information, including heat maps and session replay. Historically, web analytics has been used to refer to on-site visitor measurement. However, in recent years this meaning has become blurred, mainly because vendors are producing tools that span both categories.
Web Data Commons The Web Data Commons project extracts structured data from the Common Crawl, the largest web corpus available to the public, and provides the extracted data for public download in order to support researchers and companies in exploiting the wealth of information that is available on the Web.
Web Mining Web mining – is the application of data mining techniques to discover patterns from the Web. According to analysis targets, web mining can be divided into three different types, which are Web usage mining, Web content mining and Web structure mining.
Web Ontology Language
The Web Ontology Language (OWL) is a family of knowledge representation languages for authoring ontologies. Ontologies are a formal way to describe taxonomies and classification networks, essentially defining the structure of knowledge for various domains: the nouns representing classes of objects and the verbs representing relations between the objects. Ontologies resemble class hierarchies in object-oriented programming but there are several critical differences. Class hierarchies are meant to represent structures used in source code that evolve fairly slowly (typically monthly revisions) where as ontologies are meant to represent information on the Internet and are expected to be evolving almost constantly. Similarly, ontologies are typically far more flexible as they are meant to represent information on the Internet coming from all sorts of heterogeneous data sources. Class hierarchies on the other hand are meant to be fairly static and rely on far less diverse and more structured sources of data such as corporate databases. The OWL languages are characterized by formal semantics. They are built upon a W3C XML standard for objects called the Resource Description Framework (RDF). OWL and RDF have attracted significant academic, medical and commercial interest. In October 2007, a new W3C working group was started to extend OWL with several new features as proposed in the OWL 1.1 member submission. W3C announced the new version of OWL on 27 October 2009. This new version, called OWL 2, soon found its way into semantic editors such as Protégé and semantic reasoners such as Pellet, RacerPro, FaCT++ and HermiT. The OWL family contains many species, serializations, syntaxes and specifications with similar names. OWL and OWL2 are used to refer to the 2004 and 2009 specifications, respectively. Full species names will be used, including specification version (for example, OWL2 EL). When referring more generally, OWL Family will be used.
Web Scraping Web scraping (web harvesting or web data extraction) is a computer software technique of extracting information from websites. Usually, such software programs simulate human exploration of the World Wide Web by either implementing low-level Hypertext Transfer Protocol (HTTP), or embedding a fully-fledged web browser, such as Internet Explorer or Mozilla Firefox.
Weibull Distribution In probability theory and statistics, the Weibull distribution /ˈveɪbʊl/ is a continuous probability distribution. It is named after Waloddi Weibull, who described it in detail in 1951, although it was first identified by Fréchet (1927) and first applied by Rosin & Rammler (1933) to describe a particle size distribution.
Weight of Evidence
The Weight of Evidence or WoE value is a widely used measure of the “strength” of a grouping for separating good and bad risk (default). It is computed from the basic odds ratio: (Distribution of Good Credit Outcomes) / (Distribution of Bad Credit Outcomes). Or the ratios of Distr Goods / Distr Bads for short, where Distr refers to the proportion of Goods or Bads in the respective group, relative to the column totals, i.e., expressed as relative proportions of the total number of Goods and Bads.
Weighted Effect Coding Weighted effect coding refers to a specific coding matrix to include factor variables in generalised linear regression models. With weighted effect coding, the effect for each category represents the deviation of that category from the weighted mean (which corresponds to the sample mean). This technique has particularly attractive properties when analysing observational data, that commonly are unbalanced. The wec package is introduced, that provides functions to apply weighted effect coding to factor variables, and to interactions between (a.) a factor variable and a continuous variable and between (b.) two factor variables.
Weighted Entropy The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function.
Weighted Majority Algorithm
In machine learning, Weighted Majority Algorithm (WMA) is a meta-learning algorithm used to construct a compound algorithm from a pool of prediction algorithms, which could be any type of learning algorithms, classifiers, or even real human experts. The algorithm assumes that we have no prior knowledge about the accuracy of the algorithms in the pool, but there are sufficient reasons to believe that one or more will perform well. There are many variations of the Weighted Majority Algorithm to handle different situations, like shifting targets, infinite pools, or randomized predictions. The core mechanism remain similar, with the final performances of the compound algorithm bounded by a function of the performance of the specialist (best performing algorithm) in the pool.
Weighted Nonlinear Regression Nonlinear Least Squares
Weighted Ontology Approximation Heuristic
The present paper presents the Weighted Ontology Approximation Heuristic (WOAH), a novel zero-shot approach to ontology estimation for conversational agents development environments. This methodology extracts verbs and nouns separately from data by distilling the dependencies obtained and applying similarity and sparsity metrics to generate an ontology estimation configurable in terms of the level of generalization.
Weighted Ordered Weighted Aggregation
From a formal point of view, the WOWA operator is a particular case of Choquet integral (using a particular type of measure: a distorted probability).
Weighted Orthogonal Components Regression Analysis
In the multiple linear regression setting, we propose a general framework, termed weighted orthogonal components regression (WOCR), which encompasses many known methods as special cases, including ridge regression and principal components regression. WOCR makes use of the monotonicity inherent in orthogonal components to parameterize the weight function. The formulation allows for efficient determination of tuning parameters and hence is computationally advantageous. Moreover, WOCR offers insights for deriving new better variants. Specifically, we advocate weighting components based on their correlations with the response, which leads to enhanced predictive performance. Both simulated studies and real data examples are provided to assess and illustrate the advantages of the proposed methods.
Weighted Parallel SGD
Stochastic gradient descent (SGD) is a popular stochastic optimization method in machine learning. Traditional parallel SGD algorithms, e.g., SimuParallel SGD, often require all nodes to have the same performance or to consume equal quantities of data. However, these requirements are difficult to satisfy when the parallel SGD algorithms run in a heterogeneous computing environment; low-performance nodes will exert a negative influence on the final result. In this paper, we propose an algorithm called weighted parallel SGD (WP-SGD). WP-SGD combines weighted model parameters from different nodes in the system to produce the final output. WP-SGD makes use of the reduction in standard deviation to compensate for the loss from the inconsistency in performance of nodes in the cluster, which means that WP-SGD does not require that all nodes consume equal quantities of data. We also analyze the theoretical feasibility of running two other parallel SGD algorithms combined with WP-SGD in a heterogeneous environment. The experimental results show that WP-SGD significantly outperforms the traditional parallel SGD algorithms on distributed training systems with an unbalanced workload.
Weighted Quantile Sum
Weighted Score Table
Weighted Topological Overlaps
Weighted-SVD The Matrix Factorization models, sometimes called the latent factor models, are a family of methods in the recommender system research area to (1) generate the latent factors for the users and the items and (2) predict users’ ratings on items based on their latent factors. However, current Matrix Factorization models presume that all the latent factors are equally weighted, which may not always be a reasonable assumption in practice. In this paper, we propose a new model, called Weighted-SVD, to integrate the linear regression model with the SVD model such that each latent factor accompanies with a corresponding weight parameter. This mechanism allows the latent factors have different weights to influence the final ratings. The complexity of the Weighted-SVD model is slightly larger than the SVD model but much smaller than the SVD++ model. We compared the Weighted-SVD model with several latent factor models on five public datasets based on the Root-Mean-Squared-Errors (RMSEs). The results show that the Weighted-SVD model outperforms the baseline methods in all the experimental datasets under almost all settings.
Weight-Median Sketch We introduce a new sub-linear space data structure—the Weight-Median Sketch—that captures the most heavily weighted features in linear classifiers trained over data streams. This enables memory-limited execution of several statistical analyses over streams, including online feature selection, streaming data explanation, relative deltoid detection, and streaming estimation of pointwise mutual information. In contrast with related sketches that capture the most commonly occurring features (or items) in a data stream, the Weight-Median Sketch captures the features that are most discriminative of one stream (or class) compared to another. The Weight-Median sketch adopts the core data structure used in the Count-Sketch, but, instead of sketching counts, it captures sketched gradient updates to the model parameters. We provide a theoretical analysis of this approach that establishes recovery guarantees in the online learning setting, and demonstrate substantial empirical improvements in accuracy-memory trade-offs over alternatives, including count-based sketches and feature hashing.
Weka Weka is a collection of machine learning algorithms for data mining tasks. The algorithms can either be applied directly to a dataset or called from your own Java code. Weka contains tools for data pre-processing, classification, regression, clustering, association rules, and visualization. It is also well-suited for developing new machine learning schemes.
White Noise In signal processing, white noise is a random signal with a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustic engineering, telecommunications, statistical forecasting, and many more. White noise refers to a statistical model for signals and signal sources, rather than to any specific signal. A ‘white noise’ image. In discrete time, white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance; a single realization of white noise is a random shock. Depending on the context, one may also require that the samples be independent and have the same probability distribution (in other words i.i.d is a simplest representative of the white noise). In particular, if each sample has a normal distribution with zero mean, the signal is said to be Gaussian white noise. The samples of a white noise signal may be sequential in time, or arranged along one or more spatial dimensions. In digital image processing, the pixels of a white noise image are typically arranged in a rectangular grid, and are assumed to be independent random variables with uniform probability distribution over some interval. The concept can be defined also for signals spread over more complicated domains, such as a sphere or a torus. Some ‘white noise’ sound. An infinite-bandwidth white noise signal is a purely theoretical construction. The bandwidth of white noise is limited in practice by the mechanism of noise generation, by the transmission medium and by finite observation capabilities. Thus, a random signal is considered ‘white noise’ if it is observed to have a flat spectrum over the range of frequencies that is relevant to the context. For an audio signal, for example, the relevant range is the band of audible sound frequencies, between 20 to 20,000 Hz. Such a signal is heard as a hissing sound, resembling the /sh/ sound in ‘ash’. In music and acoustics, the term ‘white noise’ may be used for any signal that has a similar hissing sound. White noise draws its name from white light, although light that appears white generally does not have a flat spectral power density over the visible band. The term white noise is sometimes used in the context of phylogenetically based statistical methods to refer to a lack of phylogenetic pattern in comparative data. It is sometimes used in non technical contexts, in the metaphoric sense of ‘random talk without meaningful contents’.
White Noise Test
Whitening Transformation A whitening transformation is a decorrelation transformation that transforms a set of random variables having a known covariance matrix into a set of new random variables whose covariance is the identity matrix (meaning that they are uncorrelated and all have variance 1). The transformation is called “whitening” because it changes the input vector into a white noise vector. It differs from a general decorrelation transformation in that the latter only makes the covariances equal to zero, so that the correlation matrix may be any diagonal matrix. The inverse coloring transformation transforms a vector of uncorrelated variables (a white random vector) into a vector with a specified covariance matrix.
Widely Applicable Bayesian Information Criterion
A statistical model or a learning machine is called regular if the map taking a parameter to a probability distribution is one-to-one and if its Fisher information matrix is always positive definite. If otherwise, it is called singular. In regular statistical models, the Bayes free energy, which is defined by the minus logarithm of Bayes marginal likelihood, can be asymptotically approximated by the Schwarz Bayes information criterion (BIC), whereas in singular models such approximation does not hold. Recently, it was proved that the Bayes free energy of a singular model is asymptotically given by a generalized formula using a birational invariant, the real log canonical threshold (RLCT), instead of half the number of parameters in BIC. Theoretical values of RLCTs in several statistical models are now being discovered based on algebraic geometrical methodology. However, it has been difficult to estimate the Bayes free energy using only training samples, because an RLCT depends on an unknown true distribution. In the present paper, we define a widely applicable Bayesian information criterion (WBIC) by the average log likelihood function over the posterior distribution with the inverse temperature 1/logn, where n is the number of training samples. We mathematically prove that WBIC has the same asymptotic expansion as the Bayes free energy, even if a statistical model is singular for or unrealizable by a statistical model. Since WBIC can be numerically calculated without any information about a true distribution, it is a generalized version of BIC onto singular statistical models.
“Watanabe-Akaike Information Criteria”
Widely Applicable Information Criterion
“Watanabe-Akaike Information Criteria”
Wiener Process In mathematics, the Wiener process is a continuous-time stochastic process named in honor of Norbert Wiener. It is often called standard Brownian motion, after Robert Brown. It is one of the best known Lévy processes (càdlàg stochastic processes with stationary independent increments) and occurs frequently in pure and applied mathematics, economics, quantitative finance, and physics. The Wiener process plays an important role both in pure and applied mathematics. In pure mathematics, the Wiener process gave rise to the study of continuous time martingales. It is a key process in terms of which more complicated stochastic processes can be described. As such, it plays a vital role in stochastic calculus, diffusion processes and even potential theory. It is the driving process of Schramm-Loewner evolution. In applied mathematics, the Wiener process is used to represent the integral of a Gaussian white noise process, and so is useful as a model of noise in electronics engineering, instrument errors in filtering theory and unknown forces in control theory. The Wiener process has applications throughout the mathematical sciences. In physics it is used to study Brownian motion, the diffusion of minute particles suspended in fluid, and other types of diffusion via the Fokker-Planck and Langevin equations. It also forms the basis for the rigorous path integral formulation of quantum mechanics (by the Feynman-Kac formula, a solution to the Schrödinger equation can be represented in terms of the Wiener process) and the study of eternal inflation in physical cosmology. It is also prominent in the mathematical theory of finance, in particular the Black-Scholes option pricing model.
Wiener-Filter In signal processing, the Wiener Filter (Wiener-Kolmogorov Filter) is a filter used to produce an estimate of a desired or target random process by linear time-invariant filtering of an observed noisy process, assuming known stationary signal and noise spectra, and additive noise. The Wiener filter minimizes the mean square error between the estimated random process and the desired process.
Wild Scale-Enhanced Bootstrap
Wisdom of Crowds
The wisdom of the crowd is the collective opinion of a group of individuals rather than that of a single expert. A large group’s aggregated answers to questions involving quantity estimation, general world knowledge, and spatial reasoning has generally been found to be as good as, and often better than, the answer given by any of the individuals within the group. An explanation for this phenomenon is that there is idiosyncratic noise associated with each individual judgment, and taking the average over a large number of responses will go some way toward canceling the effect of this noise.[1] This process, while not new to the Information Age, has been pushed into the mainstream spotlight by social information sites such as Wikipedia, Yahoo! Answers, Quora, and other web resources that rely on human opinion.[2] Trial by jury can be understood as wisdom of the crowd, especially when compared to the alternative, trial by a judge, the single expert. In politics, sometimes sortition is held as an example of what wisdom of the crowd would look like. Decision-making would happen by a diverse group instead of by a fairly homogenous political group or party. Research within cognitive science has sought to model the relationship between wisdom of the crowd effects and individual cognition.
WoCE: a framework for clustering ensemble by exploiting the wisdom of Crowds theory
Wishart Distribution In statistics, the Wishart distribution is a generalization to multiple dimensions of the chi-squared distribution, or, in the case of non-integer degrees of freedom, of the gamma distribution. It is named in honor of John Wishart, who first formulated the distribution in 1928. It is a family of probability distributions defined over symmetric, nonnegative-definite matrix-valued random variables (“random matrices”). These distributions are of great importance in the estimation of covariance matrices in multivariate statistics. In Bayesian statistics, the Wishart distribution is the conjugate prior of the inverse covariance-matrix of a multivariate-normal random-vector.
Wishart Matrix “Wishart Distribution”
Wolfson Polarization Index affluenceIndex
Word ExtrAction for time SEries cLassification
Time series (TS) occur in many scientific and commercial applications, ranging from earth surveillance to industry automation to the smart grids. An important type of TS analysis is classification, which can, for instance, improve energy load forecasting in smart grids by detecting the types of electronic devices based on their energy consumption profiles recorded by automatic sensors. Such sensor-driven applications are very often characterized by (a) very long TS and (b) very large TS datasets needing classification. However, current methods to time series classification (TSC) cannot cope with such data volumes at acceptable accuracy; they are either scalable but offer only inferior classification quality, or they achieve state-of-the-art classification quality but cannot scale to large data volumes. In this paper, we present WEASEL (Word ExtrAction for time SEries cLassification), a novel TSC method which is both scalable and accurate. Like other state-of-the-art TSC methods, WEASEL transforms time series into feature vectors, using a sliding-window approach, which are then analyzed through a machine learning classifier. The novelty of WEASEL lies in its specific method for deriving features, resulting in a much smaller yet much more discriminative feature set. On the popular UCR benchmark of 85 TS datasets, WEASEL is more accurate than the best current non-ensemble algorithms at orders-of-magnitude lower classification and training times, and it is almost as accurate as ensemble classifiers, whose computational complexity makes them inapplicable even for mid-size datasets. The outstanding robustness of WEASEL is also confirmed by experiments on two real smart grid datasets, where it out-of-the-box achieves almost the same accuracy as highly tuned, domain-specific methods.
Word Vectors Word vectors (also referred to as distributed representations) are an amazing alternative that sweep away most of the issues of dealing with NLP. They let us ignore the difficult-to-understand grammar & syntax of language while retaining the ability to ask and answer simple questions about a text.
word2vec This tool provides an efficient implementation of the continuous bag-of-words and skip-gram architectures for computing vector representations of words. These representations can be subsequently used in many natural language processing applications and for further research.
DL4J: Word2Vec
Wordcloud A tag cloud (word cloud, or weighted list in visual design) is a visual representation for text data, typically used to depict keyword metadata (tags) on websites, or to visualize free form text. Tags are usually single words, and the importance of each tag is shown with font size or color. This format is useful for quickly perceiving the most prominent terms and for locating a term alphabetically to determine its relative prominence. When used as website navigation aids, the terms are hyperlinked to items associated with the tag.
WordNet WordNet is a lexical database for the English language. It groups English words into sets of synonyms called synsets, provides short definitions and usage examples, and records a number of relations among these synonym sets or their members. WordNet can thus be seen as a combination of dictionary and thesaurus. While it is accessible to human users via a web browser, its primary use is in automatic text analysis and artificial intelligence applications. The database and software tools have been released under a BSD style license and are freely available for download from the WordNet website. Both the lexicographic data (lexicographer files) and the compiler (called grind) for producing the distributed database are available.
Wordswarm WordSwarm generates dynamic word clouds in which the word size changes as the animation moves forward through the corpus. The top words from the preprocessing are colored randomly or from an assigned pallet, sized according to their magnitude at the first date, and then displayed in a pseudo-random location on the screen. The animation progresses into the future by growing or shrinking each word according to its frequency in the corpus at the next date. Clash detection is achieved using a 2D physics engine, which also applies ‘gravitational force’ to each word, bringing the larger words closer to the center of the screen.
Workforce Analytics Workforce analytics is a combination of software and methodology that applies statistical models to worker-related data, allowing enterprise leaders to optimize human resource management (HRM).
Write Once, Deploy Anywhere
Write Once, Run Anywhere
Write once, run anywhere’ (WORA), or sometimes write once, run everywhere (WORE), is a slogan created by Sun Microsystems to illustrate the cross-platform benefits of the Java language. Ideally, this means Java can be developed on any device, compiled into a standard bytecode and be expected to run on any device equipped with a Java virtual machine (JVM). The installation of a JVM or Java interpreter on chips, devices or software packages has become an industry standard practice. This means a programmer can develop code on a PC and can expect it to run on Java enabled cell phones, as well as on routers and mainframes equipped with Java, without any adjustments. This is intended to save software developers the effort of writing a different version of their software for each platform or operating system they intend to deploy on. This idea originated as early as in the late 1970s, when the UCSD Pascal system was developed to produce and interpret p-code. UCSD Pascal (along with the Smalltalk virtual machine) was a key influence on the design of the Java virtual machine, as is cited by James Gosling. The catch is that since there are multiple JVM implementations, on top of a wide variety of different operating systems such as Windows, Linux, Solaris, NetWare, HP-UX, and Mac OS, there can be subtle differences in how a program may execute on each JVM/OS combination, which may require an application to be tested on various target platforms. This has given rise to a joke among Java developers, ‘Write Once, Debug Everywhere’. This architecture has sometimes been criticized as ‘Saying that Java is better because it works in all platforms is like saying that Anal Sex is better because it works with all genders.’. In comparison, the Squeak Smalltalk programming language and environment, boasts as being, ‘truly write once run anywhere’, because it ‘runs bit-identical images across its wide portability base’