This paper introduces a general multi-class approach to weakly supervised classification. Inferring the labels and learning the parameters of the model is usually done jointly through a block-coordinate descent algorithm such as expectation-maximization (EM), which may lead to local minima. To avoid this problem, we propose a cost function based on a convex relaxation of the soft-max loss. We then propose an algorithm specifically designed to efficiently solve the corresponding semidefinite program (SDP). Empirically, our method compares favorably to standard ones on different datasets for multiple instance learning and semi-supervised learning as well as on clustering tasks.

Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators, where performance is evaluated using a matrix-weighted two-norm of the defect of the estimator measured with respect to the true, unknown coefficients. Two objective functions are considered depending whether the error of the defect measured with respect to the noisy coefficients is squared or unsquared. We propose simple, yet novel and theoretically well-founded data-dependent choices for the regularization parameters for both cases that avoid data-splitting. A distinguishing feature of our analysis is that we derive deterministic error bounds in terms of the error of the coefficients, thus allowing the complete separation of the analysis of the stochastic properties of these errors. We show that our results lead to new insights and bounds for linear value function estimation in reinforcement learning.

In recent years, the crucial importance of metrics in machine learning algorithms has led to an increasing interest for optimizing distance and similarity functions. Most of the state of the art focus on learning Mahalanobis distances (requiring to fulfill a constraint of positive semi-definiteness) for use in a local k-NN algorithm. However, no theoretical link is established between the learned metrics and their performance in classification. In this paper, we make use of the formal framework of good similarities introduced by Balcan et al. to design an algorithm for learning a non PSD linear similarity optimized in a nonlinear feature space, which is then used to build a global linear classifier. We show that our approach has uniform stability and derive a generalization bound on the classification error. Experiments performed on various datasets confirm the effectiveness of our approach compared to state-of-the-art methods and provide evidence that (i) it is fast, (ii) robust to overfitting and (iii) produces very sparse classifiers.

Many tasks require finding groups of elements in a matrix of numbers, symbols or class likelihoods. One approach is to use efficient bi- or tri-linear factorization techniques including PCA, ICA, sparse matrix factorization and plaid analysis. These techniques are not appropriate when addition and multiplication of matrix elements are not sensibly defined. More directly, methods like bi-clustering can be used to classify matrix elements, but these methods make the overly-restrictive assumption that the class of each element is a function of a row class and a column class. We introduce a general computational problem, `matrix tile analysis' (MTA), which consists of decomposing a matrix into a set of non-overlapping tiles, each of which is defined by a subset of usually nonadjacent rows and columns. MTA does not require an algebra for combining tiles, but must search over discrete combinations of tile assignments. Exact MTA is a computationally intractable integer programming problem, but we describe an approximate iterative technique and a computationally efficient sum-product relaxation of the integer program. We compare the effectiveness of these methods to PCA and plaid on hundreds of randomly generated tasks. Using double-gene-knockout data, we show that MTA finds groups of interacting yeast genes that have biologically-related functions.

Multitask learning algorithms are typically designed assuming some fixed, a priori known latent structure shared by all the tasks. However, it is usually unclear what type of latent task structure is the most appropriate for a given multitask learning problem. Ideally, the "right" latent task structure should be learned in a data-driven manner. We present a flexible, nonparametric Bayesian model that posits a mixture of factor analyzers structure on the tasks. The nonparametric aspect makes the model expressive enough to subsume many existing models of latent task structures (e.g, mean-regularized tasks, clustered tasks, low-rank or linear/non-linear subspace assumption on tasks, etc.). Moreover, it can also learn more general task structures, addressing the shortcomings of such models. We present a variational inference algorithm for our model. Experimental results on synthetic and real-world datasets, on both regression and classification problems, demonstrate the effectiveness of the proposed method.

Much information available on the web is copied, reused or rephrased. The phenomenon that multiple web sources pick up certain information is often called trend. A central problem in the context of web data mining is to detect those web sources that are first to publish information which will give rise to a trend. We present a simple and efficient method for finding trends dominating a pool of web sources and identifying those web sources that publish the information relevant to a trend before others. We validate our approach on real data collected from influential technology news feeds.

We show that the multi-class support vector machine (MSVM) proposed by Lee et. al. (2004), can be viewed as a MAP estimation procedure under an appropriate probabilistic interpretation of the classifier. We also show that this interpretation can be extended to a hierarchical Bayesian architecture and to a fully-Bayesian inference procedure for multi-class classification based on data augmentation. We present empirical results that show that the advantages of the Bayesian formalism are obtained without a loss in classification accuracy.

We present a hybrid algorithm for Bayesian topic models that combines the efficiency of sparse Gibbs sampling with the scalability of online stochastic inference. We used our algorithm to analyze a corpus of 1.2 million books (33 billion words) with thousands of topics. Our approach reduces the bias of variational inference and generalizes to many Bayesian hidden-variable models.

In this paper, we present a simple non-parametric method for learning the structure of undirected graphs from data that drawn from an underlying unknown distribution. We propose to use Brownian distance covariance to estimate the conditional independences between the random variables and encodes pairwise Markov graph. This framework can be applied in high-dimensional setting, where the number of parameters much be larger than the sample size.

We consider two active binary-classification problems with atypical objectives. In the first, active search, our goal is to actively uncover as many members of a given class as possible. In the second, active surveying, our goal is to actively query points to ultimately predict the proportion of a given class. Numerous real-world problems can be framed in these terms, and in either case typical model-based concerns such as generalization error are only of secondary importance. We approach these problems via Bayesian decision theory; after choosing natural utility functions, we derive the optimal policies. We provide three contributions. In addition to introducing the active surveying problem, we extend previous work on active search in two ways. First, we prove a novel theoretical result, that less-myopic approximations to the optimal policy can outperform more-myopic approximations by any arbitrary degree. We then derive bounds that for certain models allow us to reduce (in practice dramatically) the exponential search space required by a naive implementation of the optimal policy, enabling further lookahead while still ensuring that optimal decisions are always made.