Exploiting locality in probabilistic inference

This thesis investigates computational properties of decomposable probability models, which can be represented in terms of marginals over subsets of variables. We show that decomposable representations have significant locality structure that can be exploited to yield effective solutions to two important problems. The first problem is filtering in dynamic Bayesian networks, which is typically intractable because the belief state collapses to a representation with no independence structure. We present a novel technique for filtering, called thin junction tree filtering (TJTF), that approximates the belief state by a decomposable model. By exploiting locality in the belief state representation, TJTF can automatically and efficiently identify the weakest dependencies in the belief state and prune them to control the complexity of filtering. We apply TJTF to simultaneous localization and mapping, a fundamental problem in mobile robotics, and obtain a solution that performs comparably with exact methods but with substantially better time and space complexity. The second problem is distributed inference, where the nodes of a network collaborate to solve an inference problem. We present a robust architecture for distributed inference in which the nodes assemble themselves into a junction tree and solve the inference problem by message passing. In settings with unreliable communication and node failures, traditional message passing algorithms can fail because nodes cannot access the complete probability model. We present a new message passing algorithm that exploits the locality of decomposable representations to guarantee that each node can make inferences using whatever parts of the model are available. The algorithm is exact at convergence, and when parts of the model are inaccessible, its estimate is an informative approximation to the true posterior. The approach is demonstrated on the problem of automatic sensor calibration in wireless sensor networks.