Approximation structure plays an important role in inference on loopy graphs. As a tractable structure, tree approximations have been utilized in the variational method of Ghahramani & Jordan (1997) and the sequential projection method of Frey et al. (2000). However, belief propagation represents each factor of the graph with a product of single-node messages. In this paper, belief propagation is extended to represent factors with tree approximations, by way of the expectation propagation framework. That is, each factor sends a "message" to all pairs of nodes in a tree structure. The result is more accurate inferences and more frequent convergence than ordinary belief propagation, at a lower cost than variational trees or double-loop algorithms.

In applying Hidden Markov Models to the analysis of massive data streams, it is often necessary to use an artificially reduced set of states; this is due in large part to the fact that the basic HMM estimation algorithms have a quadratic dependence on the size of the state set. We present algorithms that reduce this computational bottleneck to linear or near-linear time, when the states can be embedded in an underlying grid of parameters. This type of state representation arises in many domains; in particular, we show an application to traffic analysis at a high-volume Web site.

We describe a Markov chain method for sampling from the distribution of the hidden state sequence in a nonlinear dynamical system, given a sequence of observations. This method updates all states in the sequence simultaneously using an embedded Hidden Markov Model (HMM). An update begins with the creation of "pools" of candidate states at each time. We then define an embedded HMM whose states are indexes within these pools. Using a forward-backward dynamic programming algorithm, we can efficiently choose a state sequence with the appropriate probabilities from the exponentially large number of state sequences that pass through states in these pools. We illustrate the method in a simple one-dimensional example, and in an example showing how an embedded HMM can be used to in effect discretize the state space without any discretization error. We also compare the embedded HMM to a particle smoother on a more substantial problem of inferring human motion from 2D traces of markers.

We address the problem of learning topic hierarchies from data. The model selection problem in this domain is daunting--which of the large collection of possible trees to use? We take a Bayesian approach, generating an appropriate prior via a distribution on partitions that we refer to as the nested Chinese restaurant process. This nonparametric prior allows arbitrarily large branching factors and readily accommodates growing data collections. We build a hierarchical topic model by combining this prior with a likelihood that is based on a hierarchical variant of latent Dirichlet allocation. We illustrate our approach on simulated data and with an application to the modeling of NIPS abstracts.

We develop a protocol for optimizing dynamic behavior of a network of simple electronic components, such as a sensor network, an ad hoc network of mobile devices, or a network of communication switches. This protocol requires only local communication and simple computations which are distributed among devices. The protocol is scalable to large networks. As a motivating example, we discuss a problem involving optimization of power consumption, delay, and buffer overflow in a sensor network. Our approach builds on policy gradient methods for optimization of Markov decision processes. The protocol can be viewed as an extension of policy gradient methods to a context involving a team of agents optimizing aggregate performance through asynchronous distributed communication and computation. We establish that the dynamics of the protocol approximate the solution to an ordinary differential equation that follows the gradient of the performance objective.

Recent eye tracking studies in natural tasks suggest that there is a tight link between eye movements and goal directed motor actions. However, most existing models of human eye movements provide a bottom up account that relates visual attention to attributes of the visual scene. The purpose of this paper is to introduce a new model of human eye movements that directly ties eye movements to the ongoing demands of behavior. The basic idea is that eye movements serve to reduce uncertainty about environmental variables that are task relevant. A value is assigned to an eye movement by estimating the expected cost of the uncertainty that will result if the movement is not made. If there are several candidate eye movements, the one with the highest expected value is chosen. The model is illustrated using a humanoid graphic figure that navigates on a sidewalk in a virtual urban environment. Simulations show our protocol is superior to a simple round robin scheduling mechanism.

Recent developments in grid-based and point-based approximation algorithms for POMDPs have greatly improved the tractability of POMDP planning. These approaches operate on sets of belief points by individually learning a value function for each point. In reality, belief points exist in a highly-structured metric simplex, but current POMDP algorithms do not exploit this property. This paper presents a new metric-tree algorithm which can be used in the context of POMDP planning to sort belief points spatially, and then perform fast value function updates over groups of points. We present results showing that this approach can reduce computation in point-based POMDP algorithms for a wide range of problems.

We address the problem of learning topic hierarchies from data. The model selection problem in this domain is daunting--which of the large collection of possible trees to use? We take a Bayesian approach, generating an appropriate prior via a distribution on partitions that we refer to as the nested Chinese restaurant process. This nonparametric prior allows arbitrarily large branching factors and readily accommodates growing data collections. We build a hierarchical topic model by combining this prior with a likelihood that is based on a hierarchical variant of latent Dirichlet allocation. We illustrate our approach on simulated data and with an application to the modeling of NIPS abstracts.

In this paper we present Discriminative Random Fields (DRF), a discriminative framework for the classification of natural image regions by incorporating neighborhood spatial dependencies in the labels as well as the observed data. The proposed model exploits local discriminative models and allows to relax the assumption of conditional independence of the observed data given the labels, commonly used in the Markov Random Field (MRF) framework. The parameters of the DRF model are learned using penalized maximum pseudo-likelihood method. Furthermore, the form of the DRF model allows the MAP inference for binary classification problems using the graph min-cut algorithms. The performance of the model was verified on the synthetic as well as the real-world images. The DRF model outperforms the MRF model in the experiments.

Approximate linear programming (ALP) has emerged recently as one of the most promising methods for solving complex factored MDPs with finite state spaces. In this work we show that ALP solutions are not limited only to MDPs with finite state spaces, but that they can also be applied successfully to factored continuous-state MDPs (CMDPs). We show how one can build an ALPbased approximation for such a model and contrast it to existing solution methods. We argue that this approach offers a robust alternative for solving high dimensional continuous-state space problems. The point is supported by experiments on three CMDP problems with 24-25 continuous state factors.