Quantized stochastic belief propagation: Efficient message-passing for continuous state spaces

Abstract

Belief propagation (BP) is a widely used algorithm for computing the marginal distributions in graphical models. However, in applications involving continuous random variables, the messages themselves are real-valued functions, which leads to significant computational bottlenecks. In this paper, we propose a low complexity method for performing belief propagation for continuous state space problems. Our algorithm, which we refer to as quantized stochastic belief propagation (QSBP), is a randomized variant of BP in which each node only passes stochastically chosen information at each round. The most attractive feature of QSBP is its significant gain in computational and communication efficiencies. In addition, we provide some theoretical guarantees including almost sure convergence and the rate of convergence for the case of tree-structured graphical models.

Bayesian Hypothesis Test Using Nonparametric Belief Propagation for Noisy Sparse Recovery

“…Since the signal x 0 is real valued, each BP-message takes the form of a PDF, and the BP-iteration becomes a density-messagepassing process. To implement the density-message-passing, we take the nBP approach [19]- [22]. Many nBP algorithms have been proposed according to several message sampling methods such as discarding samples having low probability density [20], adaptive sampling [21], Gibbs sampling [19], rejection sampling [22], or importance sampling [23].…”

Detection-Directed Sparse Estimation using Bayesian Hypothesis Test and Belief Propagation

“…We provide a brief summary of density-message passing in Appendix I. To implement the BP passing density-messages, we consider the sampled-message approach which has been discussed by Sudderth et al [27], and Noorshams et al [28]. For the sparse recovery, Baron et al applied the approach in [18], [19].…”

“…For implementation of BP, two approaches have been mainly discussed according to the message representation: 1) the sampled-message based BP [27], [28] where the message is directly sampled from the corresponding PDF with a certain step size such that the message is treated as a vector, and 2) the parametric-message based BP (also called relaxed BP) [23], [29], [30] where the message is described as a function with a certain set of parameters such as mean and variance. If the sampled-message approach is chosen, quantization error will be induced according to the step size.…”