Learning block structured graphs in Gaussian graphical models

Abstract

Within the framework of Gaussian graphical models, a prior distribution for the underlying graph is introduced to induce a block structure in the adjacency matrix of the graph and learning relationships between fixed groups of variables. A novel sampling strategy named Double Reversible Jumps Markov chain Monte Carlo is developed for block structural learning, under the conjugate G-Wishart prior. The algorithm proposes moves that add or remove not just a single link but an entire group of edges. The method is then applied to smooth functional data. The classical smoothing procedure is improved by placing a graphical model on the basis expansion coefficients, providing an estimate of their conditional independence structure. Since the elements of a B-Spline basis have compact support, the independence structure is reflected on well-defined portions of the domain. A known partition of the functional domain is exploited to investigate relationships among the substances within the compound.

Bayesian Learning of Graph Substructures

“…He shows empirically that joint estimation of the graph and block structure increases accuracy as compared to two-step approaches. Colombi et al (2022) and Cremaschi et al (2022) consider inference in GGMs under a known block structure with either all or no edges present between a pair of blocks.…”