Convergence analysis for Guassian belief propagation: Dynamic behaviour of marginal covariances

Tianju Sui; Damián Marelli; Minyue Fu

ICASSP 2016accepted0 citations

Convergence analysis for Guassian belief propagation: Dynamic behaviour of marginal covariances

Abstract

Despite of its wide success in many distributed statistical learning applications, the well-known Gaussian belief propagation (BP) algorithm still lacks sufficient understanding at the theoretical level. This paper studies the convergence of Gaussian BP by analyzing the dynamic behaviour of the marginal covariances. We show, under a mild technical assumption, that the information matrices (i.e., the inverses of marginal covariances) are guaranteed to converge exponentially to positive-definite matrices. The convergence rate is explicitly characterized. This result is a key step to the understanding of the dynamic behaviour of the BP iterations.

BibTeX

@inproceedings{icassp2016_convergenceanaly,
  title = {Convergence analysis for Guassian belief propagation: Dynamic behaviour of marginal covariances},
  author = {Tianju Sui and Damián Marelli and Minyue Fu},
  booktitle = {ICASSP 2016},
  year = {2016}
}