Diffusion Adaptation Strategies for Distributed Estimation over Gaussian Markov Random Fields

TL;DR

This paper introduces diffusion strategies for distributed estimation in adaptive networks that leverage Gaussian Markov random fields to account for spatial correlations, providing stability analysis and applications to sparsity recovery.

Contribution

It proposes novel diffusion algorithms that incorporate GMRF-based prior information, enabling real-time, decentralized processing with proven stability and performance analysis.

Findings

Algorithms demonstrate stable convergence in simulations.

Enhanced estimation accuracy over uncorrelated models.

Effective extension to sparsity recovery tasks.

Abstract

The aim of this paper is to propose diffusion strategies for distributed estimation over adaptive networks, assuming the presence of spatially correlated measurements distributed according to a Gaussian Markov random field (GMRF) model. The proposed methods incorporate prior information about the statistical dependency among observations, while at the same time processing data in real-time and in a fully decentralized manner. A detailed mean-square analysis is carried out in order to prove stability and evaluate the steady-state performance of the proposed strategies. Finally, we also illustrate how the proposed techniques can be easily extended in order to incorporate thresholding operators for sparsity recovery applications. Numerical results show the potential advantages of using such techniques for distributed learning in adaptive networks deployed over GMRF.