Estimation of partially known Gaussian graphical models with score-based structural priors

We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on a maximum likelihood or a maximum a posteriori criterion using (simple) priors on the precision matrix, we consider a prior on the graph and rely on annealed Langevin diffusion to generate samples from the posterior distribution. Since the Langevin sampler requires access to the score function of the underlying graph prior, we use graph neural networks to effectively estimate the score from a graph dataset (either available beforehand or generated from a known distribution). Numerical experiments demonstrate the benefits of our approach.

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

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.