Estimation of partially known Gaussian graphical models with score-based structural priors
This work addresses support estimation in graphical models for statistical inference, but it appears incremental as it builds on existing methods with a novel combination of techniques.
The paper tackles the problem of estimating partially known Gaussian graphical models by incorporating prior graph information, using annealed Langevin diffusion and graph neural networks to sample from the posterior distribution, resulting in demonstrated benefits in numerical experiments.
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.