We propose one-class support measure machines (OCSMMs) for group anomaly detection which aims at recognizing anomalous aggregate behaviors of data points. The OCSMMs generalize well-known one-class support vector machines (OCSVMs) to a space of probability measures. By formulating the problem as quantile estimation on distributions, we can establish an interesting connection to the OCSVMs and variable kernel density estimators (VKDEs) over the input space on which the distributions are defined, bridging the gap between large-margin methods and kernel density estimators. In particular, we show that various types of VKDEs can be considered as solutions to a class of regularization problems studied in this paper. Experiments on Sloan Digital Sky Survey dataset and High Energy Particle Physics dataset demonstrate the benefits of the proposed framework in real-world applications.

We study the power of different types of adaptive (nonoblivious) adversaries in the setting of prediction with expert advice, under both full-information and bandit feedback. We measure the player's performance using a new notion of regret, also known as policy regret, which better captures the adversary's adaptiveness to the player's behavior. In a setting where losses are allowed to drift, we characterize ---in a nearly complete manner--- the power of adaptive adversaries with bounded memories and switching costs. In particular, we show that with switching costs, the attainable rate with bandit feedback is $\widetilde{\Theta}(T^{2/3})$. Interestingly, this rate is significantly worse than the $\Theta(\sqrt{T})$ rate attainable with switching costs in the full-information case. Via a novel reduction from experts to bandits, we also show that a bounded memory adversary can force $\widetilde{\Theta}(T^{2/3})$ regret even in the full information case, proving that switching costs are easier to control than bounded memory adversaries. Our lower bounds rely on a new stochastic adversary strategy that generates loss processes with strong dependencies.

Major advances in Question Answering technology were needed for IBM Watson to play Jeopardy! at championship level -- the show requires rapid-fire answers to challenging natural language questions, broad general knowledge, high precision, and accurate confidence estimates. In addition, Jeopardy! features four types of decision making carrying great strategic importance: (1) Daily Double wagering; (2) Final Jeopardy wagering; (3) selecting the next square when in control of the board; (4) deciding whether to attempt to answer, i.e., "buzz in." Using sophisticated strategies for these decisions, that properly account for the game state and future event probabilities, can significantly boost a player's overall chances to win, when compared with simple "rule of thumb" strategies. This article presents our approach to developing Watson's game-playing strategies, comprising development of a faithful simulation model, and then using learning and Monte-Carlo methods within the simulator to optimize Watson's strategic decision-making. After giving a detailed description of each of our game-strategy algorithms, we then focus in particular on validating the accuracy of the simulator's predictions, and documenting performance improvements using our methods. Quantitative performance benefits are shown with respect to both simple heuristic strategies, and actual human contestant performance in historical episodes. We further extend our analysis of human play to derive a number of valuable and counterintuitive examples illustrating how human contestants may improve their performance on the show.

In systems biomedicine, an experimenter encounters different potential sources of variation in data such as individual samples, multiple experimental conditions, and multi-variable network-level responses. In multiparametric cytometry, which is often used for analyzing patient samples, such issues are critical. While computational methods can identify cell populations in individual samples, without the ability to automatically match them across samples, it is difficult to compare and characterize the populations in typical experiments, such as those responding to various stimulations or distinctive of particular patients or time-points, especially when there are many samples. Joint Clustering and Matching (JCM) is a multi-level framework for simultaneous modeling and registration of populations across a cohort. JCM models every population with a robust multivariate probability distribution. Simultaneously, JCM fits a random-effects model to construct an overall batch template -- used for registering populations across samples, and classifying new samples. By tackling systems-level variation, JCM supports practical biomedical applications involving large cohorts.

We present a family of expectation-maximization (EM) algorithms for binary and negative-binomial logistic regression, drawing a sharp connection with the variational-Bayes algorithm of Jaakkola and Jordan (2000). Indeed, our results allow a version of this variational-Bayes approach to be re-interpreted as a true EM algorithm. We study several interesting features of the algorithm, and of this previously unrecognized connection with variational Bayes. We also generalize the approach to sparsity-promoting priors, and to an online method whose convergence properties are easily established. This latter method compares favorably with stochastic-gradient descent in situations with marked collinearity.

Many machine learning algorithms assume that all input samples are independently and identically distributed from some common distribution on either the input space X, in the case of unsupervised learning, or the input and output space X x Y in the case of supervised and semi-supervised learning. In the last number of years the relaxation of this assumption has been explored and the importance of incorporation of additional information within machine learning algorithms became more apparent. Traditionally such fusion of information was the domain of semi-supervised learning. More recently the inclusion of knowledge from separate hypothetical spaces has been proposed by Vapnik as part of the supervised setting. In this work we are interested in exploring Vapnik's idea of master-class learning and the associated learning using privileged information, however within the unsupervised setting. Adoption of the advanced supervised learning paradigm for the unsupervised setting instigates investigation into the difference between privileged and technical data. By means of our proposed aRi-MAX method stability of the KMeans algorithm is improved and identification of the best clustering solution is achieved on an artificial dataset. Subsequently an information theoretic dot product based algorithm called P-Dot is proposed. This method has the ability to utilize a wide variety of clustering techniques, individually or in combination, while fusing privileged and technical data for improved clustering. Application of the P-Dot method to the task of digit recognition confirms our findings in a real-world scenario.

Although nonnegative matrix factorization (NMF) is NP-hard in general, it has been shown very recently that it is tractable under the assumption that the input nonnegative data matrix is close to being separable (separability requires that all columns of the input matrix belongs to the cone spanned by a small subset of these columns). Since then, several algorithms have been designed to handle this subclass of NMF problems. In particular, Bittorf, Recht, R\'e and Tropp (`Factoring nonnegative matrices with linear programs', NIPS 2012) proposed a linear programming model, referred to as Hottopixx. In this paper, we provide a new and more general robustness analysis of their method. In particular, we design a provably more robust variant using a post-processing strategy which allows us to deal with duplicates and near duplicates in the dataset.

In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic graphical models, deserves attention. Its simple structure - a tree - allows simple and efficient inference, while its latent variables capture complex relationships. In the past decade, the latent tree model has been subject to significant theoretical and methodological developments. In this review, we propose a comprehensive study of this model. First we summarize key ideas underlying the model. Second we explain how it can be efficiently learned from data. Third we illustrate its use within three types of applications: latent structure discovery, multidimensional clustering, and probabilistic inference. Finally, we conclude and give promising directions for future researches in this field.

Mammography is the most effective and available tool for breast cancer screening. However, the low positive predictive value of breast biopsy resulting from mammogram interpretation leads to approximately 70% unnecessary biopsies with benign outcomes. Data mining algorithms could be used to help physicians in their decisions to perform a breast biopsy on a suspicious lesion seen in a mammogram image or to perform a short term follow-up examination instead. In this research paper data mining classification algorithms; Decision Tree (DT), Artificial Neural Network (ANN), and Support Vector Machine (SVM) are analyzed on mammographic masses data set. The purpose of this study is to increase the ability of physicians to determine the severity (benign or malignant) of a mammographic mass lesion from BI-RADS attributes and the patient,s age. The whole data set is divided for training the models and test them by the ratio of 70:30% respectively and the performances of classification algorithms are compared through three statistical measures; sensitivity, specificity, and classification accuracy. Accuracy of DT, ANN and SVM are 78.12%, 80.56% and 81.25% of test samples respectively. Our analysis shows that out of these three classification models SVM predicts severity of breast cancer with least error rate and highest accuracy.

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man ifold geometry using either local or global features of the data. Building on the Laplacian Eigenmap and Diffusionmaps framework, we propose a new paradigm that offers a guarantee, under reasonable assumptions, that any manifo ld learning algorithm will preserve the geometry of a data set. Our approach is based on augmenting the output of embedding algorithms with geometric informatio n embodied in the Riemannian metric of the manifold. We provide an algorithm for estimating the Riemannian metric from data and demonstrate possible application s of our approach in a variety of examples.