This paper provides the first ---to the best of our knowledge--- analysis of online learning algorithms for multiclass problems when the {\em confusion} matrix is taken as a performance measure. The work builds upon recent and elegant results on noncommutative concentration inequalities, i.e. concentration inequalities that apply to matrices, and more precisely to matrix martingales. We do establish generalization bounds for online learning algorithm and show how the theoretical study motivate the proposition of a new confusion-friendly learning procedure. This learning algorithm, called \copa (for COnfusion Passive-Aggressive) is a passive-aggressive learning algorithm; it is shown that the update equations for \copa can be computed analytically, thus allowing the user from having to recours to any optimization package to implement it.

Approaches to audio classification and retrieval tasks largely rely on detectionbased discriminativemodels. We submit that such models make a simplistic assumption inmapping acoustics directly to semantics, whereas the actual process is likely more complex. We present a generative model that maps acoustics in a hierarchical manner to increasingly higher-level semantics. Our model has two layers with the first layer modeling generalized sound units with no clear semantic associations, while the second layer models local patterns over these sound units. We evaluate our model on a large-scale retrieval task from TRECVID 2011, and report significant improvements over standard baselines.

We derive sublinear regret bounds for undiscounted reinforcement learning in continuous state space. The proposed algorithm combines state aggregation with the use of upper confidence bounds for implementing optimism in the face of uncertainty. Beside the existence of an optimal policy which satisfies the Poisson equation, the only assumptions made are Hoelder continuity of rewards and transition probabilities.

A common challenge for Bayesian models of perception is the fact that the two fundamental Bayesian components, the prior distribution and the likelihood function, areformally unconstrained. Here we argue that a neural system that emulates Bayesian inference is naturally constrained by the way it represents sensory information inpopulations of neurons. More specifically, we show that an efficient coding principle creates a direct link between prior and likelihood based on the underlying stimulus distribution. The resulting Bayesian estimates can show biases awayfrom the peaks of the prior distribution, a behavior seemingly at odds with the traditional view of Bayesian estimation, yet one that has been reported in human perception. We demonstrate that our framework correctly accounts for the repulsive biases previously reported for the perception of visual orientation, and show that the predicted tuning characteristics of the model neurons match the reported orientation tuning properties of neurons in primary visual cortex. Our results suggest that efficient coding is a promising hypothesis in constraining Bayesianmodels of perceptual inference.

We consider the problem of performing efficient sum-product computations in an online setting over a tree. A natural application of our methods is to compute the marginal distribution at a vertex in a tree-structured Markov random field. Belief propagation can be used to solve this problem, but requires time linear in the size of the tree, and is therefore too slow in an online setting where we are continuously receiving new data and computing individual marginals. With our method we aim to update the data and compute marginals in time that is no more than logarithmic in the size of the tree, and is often significantly less. We accomplish this via a hierarchical covering structure that caches previous local sum-product computations. Our contribution is threefold: we i) give a linear time algorithm to find an optimal hierarchical cover of a tree; ii) give a sum-productlike algorithmto efficiently compute marginals with respect to this cover; and iii) apply "i" and "ii" to find an efficient algorithm with a regret bound for the online allocation problem in a multi-task setting.

Counterfactual Regret Minimization (CFR) is a popular, iterative algorithm for computing strategies in extensive-form games. The Monte Carlo CFR (MCCFR) variants reduce the per iteration time cost of CFR by traversing a smaller, sampled portion of the tree. The previous most effective instances of MCCFR can still be very slow in games with many player actions since they sample every action for a given player. In this paper, we present a new MCCFR algorithm, Average Strategy Sampling(AS), that samples a subset of the player's actions according to the player's average strategy. Our new algorithm is inspired by a new, tighter bound on the number of iterations required by CFR to converge to a given solution quality. In addition, we prove a similar, tighter bound for AS and other popular MCCFR variants.

Topic modeling is a widely used approach to analyzing large text collections. A small number of multilingual topic models have recently been explored to discover latent topics among parallel or comparable documents, such as in Wikipedia. Other topic models that were originally proposed for structured data are also applicable to multilingual documents. Correspondence Latent Dirichlet Allocation (CorrLDA) is one such model; however, it requires a pivot language to be specified in advance. We propose a new topic model, Symmetric Correspondence LDA (SymCorrLDA), that incorporates a hidden variable to control a pivot language, in an extension of CorrLDA. We experimented with two multilingual comparable datasets extracted from Wikipedia and demonstrate that SymCorrLDA is more effective than some other existing multilingual topic models.

The variational Bayesian (VB) approach is one of the best tractable approximations to the Bayesian estimation, and it was demonstrated to perform well in many applications. However, its good performance was not fully understood theoretically. For example, VB sometimes produces a sparse solution, which is regarded as a practical advantage of VB, but such sparsity is hardly observed in the rigorous Bayesian estimation. In this paper, we focus on probabilistic PCA and give more theoretical insight into the empirical success of VB. More specifically, for the situation where the noise variance is unknown, we derive a sufficient condition for perfect recovery of the true PCA dimensionality in the large-scale limit when the size of an observed matrix goes to infinity. In our analysis, we obtain bounds for a noise variance estimator and simple closed-form solutions for other parameters, which themselves are actually very useful for better implementation of VB-PCA.

This paper introduces a novel classification method for functional magnetic resonance imaging datasets with tens of classes. The method is designed to make predictions using information from as many brain locations as possible, instead of resorting to feature selection, and does this by decomposing the pattern of brain activation into differently informative sub-regions. We provide results over a complex semantic processing dataset that show that the method is competitive with state-of-the-art feature selection and also suggest how the method may be used to perform group or exploratory analyses of complex class structure.

This paper discusses the problem of calibrating posterior class probabilities from partially labelled data. Each instance is assumed to be labelled as belonging to one of several candidate categories, at most one of them being true. We generalize the concept of proper loss to this scenario, establish a necessary and sufficient condition for a loss function to be proper, and we show a direct procedure to construct a proper loss for partial labels from a conventional proper loss. The problem can be characterized by the mixing probability matrix relating the true class of the data and the observed labels. An interesting result is that the full knowledge of this matrix is not required, and losses can be constructed that are proper in a subset of the probability simplex.