Loopy Belief Propagation in the Presence of Determinism

Approximate Inference by Compilation to Arithmetic Circuits

Arithmetic circuits (ACs) exploit context-specific independence and determinism to allow exact inference even in networks with high treewidth. In this paper, we introduce the first ever approximate inference methods using ACs, for domains where exact inference remains intractable. We propose and evaluate a variety of techniques based on exact compilation, forward sampling, AC structure learning...

Very loopy belief propagation for unwrapping phase images

Since the discovery that the best error-correcting decoding algorithm can be viewed as belief propagation in a cycle-bound graph, researchers have been trying to determine under what circumstances "loopy belief propagation" is effective for probabilistic inference. Despite several theoretical advances in our understanding of loopy belief propagation, to our knowledge, the only problem that has ...

The Loopy Belief Propagation for Factor Graphs

Mathematical structures of loopy belief propagation and cluster variation method

The mathematical structures of loopy belief propagation are reviewed for graphical models in probabilistic information processing in the stand point of cluster variation method. An extension of adaptive TAP approaches is given by introducing a generalized scheme of the cluster variation method. Moreover the practical message update rules in loopy belief propagation are summarized also for quant...

Correctness of Belief Propagation in Gaussian Graphical Models of Arbitrary Topology Correctness of Belief Propagation in Gaussian Graphical Models of Arbitrary Topology

Graphical models, such as Bayesian networks and Markov random elds represent statistical dependencies of variables by a graph. Local \belief propagation" rules of the sort proposed by Pearl [20] are guaranteed to converge to the correct posterior probabilities in singly connected graphs. Recently good performance has been obtained by using these same rules on graphs with loops, a method known a...