Belief Propagation for Continuous State Spaces: Stochastic Message-Passing with Quantitative Guarantees
Year: 2012
Type: preprint
Abstract: The sum-product or belief propagation (BP) algorithm is a widely used message-passing technique for computing approximate marginals in graphical models. We introduce a new technique, called stochastic orthogonal series message-passing (SOSMP), for computing the BP fixed point in models with continuous random variables. It is based on a deterministic approximation of the messages via orthogonal series expansion, and a stochastic approximation via Monte Carlo estimates of the integral updates of the basis coefficients. We prove that the SOSMP iterates converge to a δ-neighborhood of the unique BP fixed point for any tree-structured graph, and for any graphs with cycles in which the BP updates satisfy a contractivity condition. In addition, we demonstrate how to choose the number of basis coefficients as a function of the desired approximation accuracy δand smoothness of the compatibility functions. We illustrate our theory with both simulated examples and in application to optical flow estimation.
Source: arXiv (Cornell University)
Authors: Noorshams, Nima, Wainwright, Martin J.
Institution: University of California, Berkeley
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2103156296