We present a new anytime algorithm that achieves near-optimal regret for any instance of finite stochastic partial monitoring. In particular, the new algorithm achieves the minimax regret, within logarithmic factors, for both "easy" and "hard" problems. For easy problems, it additionally achieves logarithmic individual regret. Most importantly, the algorithm is adaptive in the sense that if the opponent strategy is in an "easy region" of the strategy space then the regret grows as if the problem was easy. As an implication, we show that under some reasonable additional assumptions, the algorithm enjoys an O(\sqrt{T}) regret in Dynamic Pricing, proven to be hard by Bartok et al. (2011).

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.

Feature selection and regularization are becoming increasingly prominent tools in the efforts of the reinforcement learning (RL) community to expand the reach and applicability of RL. One approach to the problem of feature selection is to impose a sparsity-inducing form of regularization on the learning method. Recent work on $L_1$ regularization has adapted techniques from the supervised learning literature for use with RL. Another approach that has received renewed attention in the supervised learning community is that of using a simple algorithm that greedily adds new features. Such algorithms have many of the good properties of the $L_1$ regularization methods, while also being extremely efficient and, in some cases, allowing theoretical guarantees on recovery of the true form of a sparse target function from sampled data. This paper considers variants of orthogonal matching pursuit (OMP) applied to reinforcement learning. The resulting algorithms are analyzed and compared experimentally with existing $L_1$ regularized approaches. We demonstrate that perhaps the most natural scenario in which one might hope to achieve sparse recovery fails; however, one variant, OMP-BRM, provides promising theoretical guarantees under certain assumptions on the feature dictionary. Another variant, OMP-TD, empirically outperforms prior methods both in approximation accuracy and efficiency on several benchmark problems.

We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be applied to attributed graphs, our approach allows to rate mappings of subgraphs by a flexible scoring scheme comparing vertex and edge attributes by kernels. We show that subgraph matching kernels generalize several known kernels. To compute the kernel we propose a graph-theoretical algorithm inspired by a classical relation between common subgraphs of two graphs and cliques in their product graph observed by Levi (1973). Encouraging experimental results on a classification task of real-world graphs are presented.

Latent feature models are attractive for image modeling, since images generally contain multiple objects. However, many latent feature models ignore that objects can appear at different locations or require pre-segmentation of images. While the transformed Indian buffet process (tIBP) provides a method for modeling transformation-invariant features in unsegmented binary images, its current form is inappropriate for real images because of its computational cost and modeling assumptions. We combine the tIBP with likelihoods appropriate for real images and develop an efficient inference, using the cross-correlation between images and features, that is theoretically and empirically faster than existing inference techniques. Our method discovers reasonable components and achieve effective image reconstruction in natural images.

LSTD is a popular algorithm for value function approximation. Whenever the number of features is larger than the number of samples, it must be paired with some form of regularization. In particular, L1-regularization methods tend to perform feature selection by promoting sparsity, and thus, are well-suited for high-dimensional problems. However, since LSTD is not a simple regression algorithm, but it solves a fixed--point problem, its integration with L1-regularization is not straightforward and might come with some drawbacks (e.g., the P-matrix assumption for LASSO-TD). In this paper, we introduce a novel algorithm obtained by integrating LSTD with the Dantzig Selector. We investigate the performance of the proposed algorithm and its relationship with the existing regularized approaches, and show how it addresses some of their drawbacks.

Conditional modeling x \to y is a central problem in machine learning. A substantial research effort is devoted to such modeling when x is high dimensional. We consider, instead, the case of a high dimensional y, where x is either low dimensional or high dimensional. Our approach is based on selecting a small subset y_L of the dimensions of y, and proceed by modeling (i) x \to y_L and (ii) y_L \to y. Composing these two models, we obtain a conditional model x \to y that possesses convenient statistical properties. Multi-label classification and multivariate regression experiments on several datasets show that this model outperforms the one vs. all approach as well as several sophisticated multiple output prediction methods.

In this paper, a novel learning paradigm is presented to automatically identify groups of informative and correlated features from very high dimensions. Specifically, we explicitly incorporate correlation measures as constraints and then propose an efficient embedded feature selection method using recently developed cutting plane strategy. The benefits of the proposed algorithm are twofolds. First, it can identify the optimal discriminative and uncorrelated feature subset to the output labels, denoted here as Support Features, which brings about significant improvements in prediction performance over other state of the art feature selection methods considered in the paper. Second, during the learning process, the underlying group structures of correlated features associated with each support feature, denoted as Affiliated Features, can also be discovered without any additional cost. These affiliated features serve to improve the interpretations on the learning tasks. Extensive empirical studies on both synthetic and very high dimensional real-world datasets verify the validity and efficiency of the proposed method. To address this issue, a plethora of feature selection methods have been developed in the recent decades.

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.

The paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time. Such structures arise in the context of social networks or protein interactions where underlying graphs have adjacency matrices which are block-diagonal in the appropriate basis. We introduce a convex mixed penalty which involves $\ell_1$-norm and trace norm simultaneously. We obtain an oracle inequality which indicates how the two effects interact according to the nature of the target matrix. We bound generalization error in the link prediction problem. We also develop proximal descent strategies to solve the optimization problem efficiently and evaluate performance on synthetic and real data sets.