Gaussian Belief with dynamic data and in dynamic network

TL;DR

This paper analyzes Gaussian belief propagation in dynamic environments, showing its scalability and effectiveness in large, fluctuating networks through spectral analysis and numerical results.

Contribution

It introduces a spectral analysis framework for Gaussian belief propagation in dynamic networks, demonstrating its scalability and robustness in fluctuating systems.

Findings

Spectral gap persists in large Erdos-Renyi graphs, indicating good scalability.

Averaging is more effective in dynamic networks than in dynamic data scenarios.

Methods perform well in very large, dynamic information systems.

Abstract

In this paper we analyse Belief Propagation over a Gaussian model in a dynamic environment. Recently, this has been proposed as a method to average local measurement values by a distributed protocol ("Consensus Propagation", Moallemi & Van Roy, 2006), where the average is available for read-out at every single node. In the case that the underlying network is constant but the values to be averaged fluctuate ("dynamic data"), convergence and accuracy are determined by the spectral properties of an associated Ruelle-Perron-Frobenius operator. For Gaussian models on Erdos-Renyi graphs, numerical computation points to a spectral gap remaining in the large-size limit, implying exceptionally good scalability. In a model where the underlying network also fluctuates ("dynamic network"), averaging is more effective than in the dynamic data case. Altogether, this implies very good performance of these methods in very large systems, and opens a new field of statistical physics of large (and dynamic) information systems.