Statistical Graph Signal Recovery Using Variational Bayes

TL;DR

This paper introduces a Bayesian Variational Bayes method for graph signal recovery that estimates the graph topology and signal simultaneously, even when the graph is initially unknown, demonstrating superior performance on synthetic and real data.

Contribution

It develops a novel Bayesian approach with a new GCCH distribution for adjacency matrix posteriors, enabling effective graph signal recovery without prior graph knowledge.

Findings

Outperforms existing algorithms in accuracy

Accurately estimates graph topology and noise variance

Validates effectiveness on synthetic and real-world data

Abstract

This paper investigates the problem of graph signal recovery (GSR) when the topology of the graph is not known in advance. In this paper, the elements of the weighted adjacency matrix is statistically related to normal distribution and the graph signal is assumed to be Gaussian Markov Random Field (GMRF). Then, the problem of GSR is solved by a Variational Bayes (VB) algorithm in a Bayesian manner by computing the posteriors in a closed form. The posteriors of the elements of weighted adjacency matrix are proved to have a new distribution which we call it generalized compound confluent hypergeometric (GCCH) distribution. Moreover, the variance of the noise is estimated by calculating its posterior via VB. The simulation results on synthetic and real-world data shows the superiority of the proposed Bayesian algorithm over some state-of-the-art algorithms in recovering the graph signal.