We present a class of algorithms for learning the structure of graphical models from data. The algorithms are based on a measure known as the kernel generalized variance (KGV), which essentially allows us to treat all variables on an equal footing as Gaussians in a feature space obtained from Mercer kernels. Thus we are able to learn hybrid graphs involving discrete and continuous variables of arbitrary type. We explore the computational properties of our approach, showing how to use the kernel trick to compute the relevant statistics in linear time. We illustrate our framework with experiments involving discrete and continuous data.

We present a new method for learning good strategies in zero-sum Markov games in which each side is composed of multiple agents collaborating against an opposing team of agents. Our method requires full observability and communication during learning, but the learned policies can be executed in a distributed manner. The value function is represented as a factored linear architecture and its structure determines the necessary computational resources and communication bandwidth. This approach permits a tradeoff between simple representations with little or no communication between agents and complex, computationally intensive representations with extensive coordination between agents. Thus, we provide a principled means of using approximation to combat the exponential blowup in the joint action space of the participants. The approach is demonstrated with an example that shows the efficiency gains over naive enumeration.

We consider Bayesian mixture approaches, where a predictor is constructed by forming a weighted average of hypotheses from some space of functions. While such procedures are known to lead to optimal predictors in several cases, where sufficiently accurate prior information is available, it has not been clear how they perform when some of the prior assumptions are violated. In this paper we establish data-dependent bounds for such procedures, extending previous randomized approaches such as the Gibbs algorithm to a fully Bayesian setting. The finite-sample guarantees established in this work enable the utilization of Bayesian mixture approaches in agnostic settings, where the usual assumptions of the Bayesian paradigm fail to hold. Moreover, the bounds derived can be directly applied to non-Bayesian mixture approaches such as Bagging and Boosting.

Convergence for iterative reinforcement learning algorithms like TD(O) depends on the sampling strategy for the transitions. However, in practical applications it is convenient to take transition data from arbitrary sources without losing convergence. In this paper we investigate the problem of repeated synchronous updates based on a fixed set of transitions. Our main theorem yields sufficient conditions of convergence for combinations of reinforcement learning algorithms and linear function approximation. This allows to analyse if a certain reinforcement learning algorithm and a certain function approximator are compatible.

An essential step in understanding the function of sensory nervous systems is to characterize as accurately as possible the stimulus-response function (SRF) of the neurons that relay and process sensory information. One increasingly common experimental approach is to present a rapidly varying complex stimulus to the animal while recording the responses of one or more neurons, and then to directly estimate a functional transformation of the input that accounts for the neuronal firing. The estimation techniques usually employed, such as Wiener filtering or other correlation-based estimation of the Wiener or Volterra kernels, are equivalent to maximum likelihood estimation in a Gaussian-output-noise regression model. We explore the use of Bayesian evidence-optimization techniques to condition these estimates. We show that by learning hyperparameters that control the smoothness and sparsity of the transfer function it is possible to improve dramatically the quality of SRF estimates, as measured by their success in predicting responses to novel input.

We present a framework for sparse Gaussian process (GP) methods which uses forward selection with criteria based on informationtheoretic principles, previously suggested for active learning. Our goal is not only to learn d-sparse predictors (which can be evaluated in O(d) rather than O(n), d n, n the number of training points), but also to perform training under strong restrictions on time and memory requirements.

The Bayesian paradigm provides a natural and effective means of exploiting prior knowledge concerning the time-frequency structure of sound signals such as speech and music--something which has often been overlooked in traditional audio signal processing approaches. Here, after constructing a Bayesian model and prior distributions capable of taking into account the time-frequency characteristics of typical audio waveforms, we apply Markov chain Monte Carlo methods in order to sample from the resultant posterior distribution of interest. We present speech enhancement results which compare favourably in objective terms with standard time-varying filtering techniques (and in several cases yield superior performance, both objectively and subjectively); moreover, in contrast to such methods, our results are obtained without an assumption of prior knowledge of the noise power.

We describe a method for computing provably exact maximum a posteriori (MAP) estimates for a subclass of problems on graphs with cycles. The basic idea is to represent the original problem on the graph with cycles as a convex combination of tree-structured problems. A convexity argument then guarantees that the optimal value of the original problem (i.e., the log probability of the MAP assignment) is upper bounded by the combined optimal values of the tree problems. We prove that this upper bound is met with equality if and only if the tree problems share an optimal configuration in common. An important implication is that any such shared configuration must also be the MAP configuration for the original problem. Next we develop a tree-reweighted max-product algorithm for attempting to find convex combinations of tree-structured problems that share a common optimum. We give necessary and sufficient conditions for a fixed point to yield the exact MAP estimate. An attractive feature of our analysis is that it generalizes naturally to convex combinations of hypertree-structured distributions.

In this paper, we consider Tipping's relevance vector machine (RVM) [1] and formalize an incremental training strategy as a variant of the expectation-maximization (EM) algorithm that we call Subspace EM (SSEM). Working with a subset of active basis functions, the sparsity of the RVM solution will ensure that the number of basis functions and thereby the computational complexity is kept low. We also introduce a mean field approach to the intractable classification model that is expected to give a very good approximation to exact Bayesian inference and contains the Laplace approximation as a special case.

Well-known applications include part-of-speech (POS) tagging, named entity classification, information extraction, text segmentation and phoneme classification in text and speech processing [7] as well as problems like protein homology detection, secondary structure prediction or gene classification in computational biology [3]. Up to now, the predominant formalism for modeling and predicting label sequences has been based on Hidden Markov Models (HMMs) and variations thereof. Yet, despite its success, generative probabilistic models - of which HMMs are a special case - have two major shortcomings, which this paper is not the first one to point out. First, generative probabilistic models are typically trained using maximum likelihood estimation (MLE) for a joint sampling model of observation and label sequences. As has been emphasized frequently, MLE based on the joint probability model is inherently non-discriminative and thus may lead to suboptimal prediction accuracy. Secondly, efficient inference and learning in this setting often requires to make questionable conditional independence assumptions.