We describe a model based on a Boltzmann machine with third-order connections that can learn how to accumulate information about a shape over several fixations. The model uses a retina that only has enough high resolution pixels to cover a small area of the image, so it must decide on a sequence of fixations and it must combine the glimpse" at each fixation with the location of the fixation before integrating the information with information from other glimpses of the same object. We evaluate this model on a synthetic dataset and two image classification datasets, showing that it can perform at least as well as a model trained on whole images." Papers published at the Neural Information Processing Systems Conference.

While many perceptual and cognitive phenomena are well described in terms of Bayesian inference, the necessary computations are intractable at the scale of real-world tasks, and it remains unclear how the human mind approximates Bayesian inference algorithmically. We explore the proposal that for some tasks, humans use a form of Markov Chain Monte Carlo to approximate the posterior distribution over hidden variables. As a case study, we show how several phenomena of perceptual multistability can be explained as MCMC inference in simple graphical models for low-level vision. Papers published at the Neural Information Processing Systems Conference.

We propose a new probabilistic model for analyzing dynamic evolutions of relational data, such as additions, deletions and split & merge, of relation clusters like communities in social networks. Our proposed model abstracts observed time-varying object-object relationships into relationships between object clusters. We extend the infinite Hidden Markov model to follow dynamic and time-sensitive changes in the structure of the relational data and to estimate a number of clusters simultaneously. We show the usefulness of the model through experiments with synthetic and real-world data sets. Papers published at the Neural Information Processing Systems Conference.

The Partially Observable Markov Decision Process (POMDP) framework has proven useful in planning domains that require balancing actions that increase an agents knowledge and actions that increase an agents reward. Unfortunately, most POMDPs are complex structures with a large number of parameters. In many realworld problems, both the structure and the parameters are difficult to specify from domain knowledge alone. Recent work in Bayesian reinforcement learning has made headway in learning POMDP models; however, this work has largely focused on learning the parameters of the POMDP model. We define an infinite POMDP (iPOMDP) model that does not require knowledge of the size of the state space; instead, it assumes that the number of visited states will grow as the agent explores its world and explicitly models only visited states.

Our setting is a Partially Observable Markov Decision Process with continuous state, observation and action spaces. Decisions are based on a Particle Filter for estimating the belief state given past observations. We consider a policy gradient approach for parameterized policy optimization. For that purpose, we investigate sensitivity analysis of the performance measure with respect to the parameters of the policy, focusing on Finite Difference (FD) techniques. We show that the naive FD is subject to variance explosion because of the non-smoothness of the resampling procedure.

This paper considers a sensitivity analysis in Hidden Markov Models with continuous state and observation spaces. We propose an Infinitesimal Perturbation Analysis (IPA) on the filtering distribution with respect to some parameters of the model. We describe a methodology for using any algorithm that estimates the filtering density, such as Sequential Monte Carlo methods, to design an algorithm that estimates its gradient. The resulting IPA estimator is proven to be asymptotically unbiased, consistent and has computational complexity linear in the number of particles. We consider an application of this analysis to the problem of identifying unknown parameters of the model given a sequence of observations.

A fundamental objective in reinforcement learning is the maintenance of a proper balance between exploration and exploitation. This problem becomes more challenging when the agent can only partially observe the states of its environment. In this paper we propose a dual-policy method for jointly learning the agent behavior and the balance between exploration exploitation, in partially observable environments. The method subsumes traditional exploration, in which the agent takes actions to gather information about the environment, and active learning, in which the agent queries an oracle for optimal actions (with an associated cost for employing the oracle). The form of the employed exploration is dictated by the specific problem.

We present a system which constructs a topological map of an environment given a sequence of images. This system includes a novel image similarity score which uses dynamic programming to match images using both the appearance and relative positions of local features simultaneously. Additionally an MRF is constructed to model the probability of loop-closures. A locally optimal labeling is found using Loopy-BP. Finally we outline a method to generate a topological map from loop closure data.

We present an algorithm for learning high-treewidth Markov networks where inference is still tractable. This is made possible by exploiting context specific independence and determinism in the domain. The class of models our algorithm can learn has the same desirable properties as thin junction trees: polynomial inference, closed form weight learning, etc., but is much broader. Our algorithm searches for a feature that divides the state space into subspaces where the remaining variables decompose into independent subsets (conditioned on the feature or its negation) and recurses on each subspace/subset of variables until no useful new features can be found. We provide probabilistic performance guarantees for our algorithm under the assumption that the maximum feature length is k (the treewidth can be much larger) and dependences are of bounded strength.

Straightforward application of Deep Belief Nets (DBNs) to acoustic modeling produces a rich distributed representation of speech data that is useful for recognition and yields impressive results on the speaker-independent TIMIT phone recognition task. However, the first-layer Gaussian-Bernoulli Restricted Boltzmann Machine (GRBM) has an important limitation, shared with mixtures of diagonal-covariance Gaussians: GRBMs treat different components of the acoustic input vector as conditionally independent given the hidden state. The mean-covariance restricted Boltzmann machine (mcRBM), first introduced for modeling natural images, is a much more representationally efficient and powerful way of modeling the covariance structure of speech data. Every configuration of the precision units of the mcRBM specifies a different precision matrix for the conditional distribution over the acoustic space. In this work, we use the mcRBM to learn features of speech data that serve as input into a standard DBN.