This paper presents a new framework based on walks in a graph for analysis andinference in Gaussian graphical models. The key idea is to decompose correlationsbetween variables as a sum over all walks between those variables in the graph. The weight of each walk is given by a product of edgewise partial correlations. We provide a walk-sum interpretation ofGaussian belief propagation in trees and of the approximate method of loopy belief propagation in graphs with cycles.

We describe a three-dimensional geometric hand model suitable for visual trackingapplications. The kinematic constraints implied by the model's joints have a probabilistic structure which is well described by a graphical model. Inference in this model is complicated by the hand's many degrees of freedom, as well as multimodal likelihoods caused by ambiguous image measurements. We use nonparametric belief propagation (NBP)to develop a tracking algorithm which exploits the graph's structure to control complexity, while avoiding costly discretization. While kinematic constraints naturally have a local structure, self-occlusions created by the imaging process lead to complex interpendencies incolor and edge-based likelihood functions. However, we show that local structure may be recovered by introducing binary hidden variables describingthe occlusion state of each pixel. We augment the NBP algorithm to infer these occlusion variables in a distributed fashion, and then analytically marginalize over them to produce hand position estimates whichproperly account for occlusion events. We provide simulations showing that NBP may be used to refine inaccurate model initializations, aswell as track hand motion through extended image sequences.

We introduce a computationally efficient method to estimate the validity of the BP method as a function of graph topology, the connectivity strength, frustration and network size.

Mitchell and Levesque provide commentary on the two AAAI Classic Paper awards, given at the AAAI-05 conference in Pittsburgh, Pennsylvania. The two winning papers were "Quantifying the Inductive Bias in Concept Learning," by David Haussler, and "Default Reasoning, Nonmonotonic Logics, and the Frame Problem," by Steve Hanks and Drew McDermott.

This paper extends the framework of partially observable Markov decision processes (POMDPs) to multi-agent settings by incorporating the notion of agent models into the state space. Agents maintain beliefs over physical states of the environment and over models of other agents, and they use Bayesian updates to maintain their beliefs over time. The solutions map belief states to actions. Models of other agents may include their belief states and are related to agent types considered in games of incomplete information. We express the agents' autonomy by postulating that their models are not directly manipulable or observable by other agents. We show that important properties of POMDPs, such as convergence of value iteration, the rate of convergence, and piece-wise linearity and convexity of the value functions carry over to our framework. Our approach complements a more traditional approach to interactive settings which uses Nash equilibria as a solution paradigm. We seek to avoid some of the drawbacks of equilibria which may be non-unique and do not capture off-equilibrium behaviors. We do so at the cost of having to represent, process and continuously revise models of other agents. Since the agent's beliefs may be arbitrarily nested, the optimal solutions to decision making problems are only asymptotically computable. However, approximate belief updates and approximately optimal plans are computable. We illustrate our framework using a simple application domain, and we show examples of belief updates and value functions.

Belief propagation on cyclic graphs is an efficient algorithm for computing approximate marginal probability distributions over single nodes and neighboring nodes in the graph. In this paper we propose two new algorithms for approximating joint probabilities of arbitrary pairs of nodes and prove a number of desirable properties that these estimates fulfill. The first algorithm is a propagation algorithm which is shown to converge if belief propagation converges to a stable fixed point. The second algorithm is based on matrix inversion. Experiments compare a number of competing methods.

The detection and pose estimation of people in images and video is made challenging by the variability of human appearance, the complexity of natural scenes, and the high dimensionality of articulated body models. To cope with these problems we represent the 3D human body as a graphical model in which the relationships between the body parts are represented by conditional probability distributions. We formulate the pose estimation problem as one of probabilistic inference over a graphical model where the random variables correspond to the individual limb parameters (position and orientation). Because the limbs are described by 6-dimensional vectors encoding pose in 3-space, discretization is impractical and the random variables in our model must be continuousvalued. To approximate belief propagation in such a graph we exploit a recently introduced generalization of the particle filter. This framework facilitates the automatic initialization of the body-model from low level cues and is robust to occlusion of body parts and scene clutter.

The detection and pose estimation of people in images and video is made challenging by the variability of human appearance, the complexity of natural scenes, and the high dimensionality of articulated body models. Tocope with these problems we represent the 3D human body as a graphical model in which the relationships between the body parts are represented by conditional probability distributions. We formulate the pose estimation problem as one of probabilistic inference over a graphical modelwhere the random variables correspond to the individual limb parameters (position and orientation). Because the limbs are described by 6-dimensional vectors encoding pose in 3-space, discretization is impractical andthe random variables in our model must be continuousvalued. To approximate belief propagation in such a graph we exploit a recently introduced generalization of the particle filter. This framework facilitates the automatic initialization of the body-model from low level cues and is robust to occlusion of body parts and scene clutter.

An accepted belief is a proposition considered likely enough by an agent, to be inferred from as if it were true. This paper bridges the gap between probabilistic and logical representations of accepted beliefs. To this end, natural properties of relations on propositions, describing relative strength of belief are augmented with some conditions ensuring that accepted beliefs form a deductively closed set. This requirement turns out to be very restrictive. In particular, it is shown that the sets of accepted belief of an agent can always be derived from a family of possibility rankings of states. An agent accepts a proposition in a given context if this proposition is considered more possible than its negation in this context, for all possibility rankings in the family. These results are closely connected to the non-monotonic 'preferential' inference system of Kraus, Lehmann and Magidor and the so-called plausibility functions of Friedman and Halpern. The extent to which probability theory is compatible with acceptance relations is laid bare. A solution to the lottery paradox, which is considered as a major impediment to the use of non-monotonic inference is proposed using a special kind of probabilities (called lexicographic, or big-stepped). The setting of acceptance relations also proposes another way of approaching the theory of belief change after the works of Gärdenfors and colleagues. Our view considers the acceptance relation as a primitive object from which belief sets are derived in various contexts.

We consider loopy belief propagation for approximate inference in probabilistic graphical models. A limitation of the standard algorithm is that clique marginals are computed as if there were no loops in the graph. To overcome this limitation, we introduce fractional belief propagation. Fractional belief propagation is formulated in terms of a family of approximate free energies, which includes the Bethe free energy and the naive mean-field free as special cases. Using the linear response correction of the clique marginals, the scale parameters can be tuned. Simulation results illustrate the potential merits of the approach.