Bayesian topology inference on partially known networks from input-output pairs

TL;DR

This paper introduces a Bayesian sampling method for system identification in partially known networks using input-output data, leveraging graph neural networks to incorporate prior information and improve estimation accuracy.

Contribution

It presents a novel Bayesian sampling algorithm based on annealed Langevin diffusion for network system identification with partial prior knowledge.

Findings

Sampling-based approach outperforms classical point estimation methods.

Incorporating prior graph information via neural networks improves accuracy.

Method effective on both real-world and synthetic networks.

Abstract

We propose a sampling algorithm to perform system identification from a set of input-output graph signal pairs. The dynamics of the systems we study are given by a partially known adjacency matrix and a generic parametric graph filter of unknown parameters. The methodology we employ is built upon the principles of annealed Langevin diffusion. This enables us to draw samples from the posterior distribution instead of following the classical approach of point estimation using maximum likelihood. We investigate how to harness the prior information inherent in a dataset of graphs of different sizes through the utilization of graph neural networks. We demonstrate, via numerical experiments involving both real-world and synthetic networks, that integrating prior knowledge into the estimation process enhances estimation performance.