Convergence Analysis of Gaussian Belief Propagation: Dynamic Behaviour of Marginal Covariances

DAMIÁN MARELLI; TIANJU SUI; MINYUE FU

Shanghai

Conferencia; IEEE Conference on on Acoustics, Speech, and Signal Processing (ICASSP); 2016

Institute of Electrical and Electronics Engineers (IEEE)

Despite of its wide success in many distributedstatistical learning applications, the well-known Gaussian beliefpropagation (BP) algorithm still lacks sufficient understandingat the theoretical level. This paper studies the convergenceof Gaussian BP by analyzing the dynamic behaviour of themarginal covariances. We show, under a mild technical as-sumption, that the information matrices (i.e., the inverses ofmarginal covariances) are guaranteed to converge exponentiallyto positive-definite matrices. The convergence rate is explicitlycharacterized. This result is a key step to the understanding ofthe dynamic behaviour of the BP iterations.