Policy gradient methods are reinforcement learning algorithms that adapt a parameterized policyby following a performance gradient estimate. Conventional policy gradient methods use Monte-Carlo techniques to estimate this gradient. Since Monte Carlo methods tend to have high variance, a large number of samples is required, resulting in slow convergence. In this paper, we propose a Bayesian framework that models the policy gradient as a Gaussian process. This reduces the number of samples needed to obtain accurate gradient estimates. Moreover, estimates of the natural gradient as well as a measure of the uncertainty in the gradient estimates are provided at little extra cost.

Multinomial logistic regression provides the standard penalised maximum-likelihood solution to multi-Class pattern recognition problems.

Another recent innovation is the use of long and rich stimuli in MRI experiments, such as a commercial movie [8], rather than the traditional controlled, repeating simple stimuli.

The ill-posed nature of the MEG/EEG source localization problem requires the incorporation of prior assumptions when choosing an appropriate solution out of an infinite set of candidates. Bayesian methods are useful in this capacity because they allow these assumptions to be explicitly quantified. Recently, a number of empirical Bayesian approaches have been proposed that attempt a form of model selection by using the data to guide the search for an appropriate prior. While seemingly quite different in many respects, we apply a unifying framework based on automatic relevance determination (ARD) that elucidates various attributes of these methods and suggests directions for improvement. We also derive theoretical propertiesof this methodology related to convergence, local minima, and localization bias and explore connections with established algorithms.

We present a method for localizing and separating sound sources in stereo recordings thatis robust to reverberation and does not make any assumptions about the source statistics. The method consists of a probabilistic model of binaural multisource recordingsand an expectation maximization algorithm for finding the maximum likelihood parameters of that model. These parameters include distributions over delays and assignments of time-frequency regions to sources. We evaluate this method against two comparable algorithms on simulations of simultaneous speech from two or three sources. Our method outperforms the others in anechoic conditionsand performs as well as the better of the two in the presence of reverberation.

We consider the problem of inferring the structure of a network from cooccurrence data:observations that indicate which nodes occur in a signaling pathway but do not directly reveal node order within the pathway. This problem is motivated by network inference problems arising in computational biology and communication systems, in which it is difficult or impossible to obtain precise time ordering information. Without order information, every permutation of the activated nodes leads to a different feasible solution, resulting in combinatorial explosion of the feasible set. However, physical principles underlying most networked systemssuggest that not all feasible solutions are equally likely. Intuitively, nodes that cooccur more frequently are probably more closely connected. Building on this intuition, we model path co-occurrences as randomly shuffled samples of a random walk on the network. We derive a computationally efficient network inference algorithm and, via novel concentration inequalities for importance samplingestimators, prove that a polynomial complexity Monte Carlo version of the algorithm converges with high probability.

Many noninvasive techniques have emerged for functional brain mapping, such as functional magnetic resonance imaging (MRI) and electromagnetic source imaging (ESI).

We describe an unsupervised method for learning a probabilistic grammar of an object from a set of training examples. Our approach is invariant to the scale and rotation of the objects. We illustrate our approach using thirteen objects from the Caltech 101 database. In addition, we learn the model of a hybrid object class where we do not know the specific object or its position, scale or pose. This is illustrated bylearning a hybrid class consisting of faces, motorbikes, and airplanes. The individual objects can be recovered as different aspects of the grammar for the object class.

Finite mixture model is a powerful tool in many statistical learning problems. In this paper, we propose a general, structure-preserving approach to reduce its model complexity, which can bring significant computational benefits in many applications. The basic idea is to group the original mixture components into compact clusters, and then minimize an upper bound on the approximation error between the original and simplified models.

We introduce a Gaussian process (GP) framework, stochastic relational models (SRM), for learning social, physical, and other relational phenomena where interactions betweenentities are observed. The key idea is to model the stochastic structure of entity relationships (i.e., links) via a tensor interaction of multiple GPs, each defined on one type of entities. These models in fact define a set of nonparametric priors on infinite dimensional tensor matrices, where each element represents a relationship between a tuple of entities. By maximizing the marginalized likelihood,information is exchanged between the participating GPs through the entire relational network, so that the dependency structure of links is messaged to the dependency of entities, reflected by the adapted GP kernels. The framework offers a discriminative approach to link prediction, namely, predicting the existences, strengths,or types of relationships based on the partially observed linkage network as well as the attributes of entities (if given). We discuss properties and variants of SRM and derive an efficient learning algorithm. Very encouraging experimental resultsare achieved on a toy problem and a user-movie preference link prediction task. In the end we discuss extensions of SRM to general relational learning tasks.