Learning block structured graphs in Gaussian graphical models

TL;DR

This paper introduces a new Bayesian method for learning block-structured Gaussian graphical models, using a novel Markov chain Monte Carlo algorithm to efficiently identify group-based relationships in complex data.

Contribution

It develops a Double Reversible Jumps MCMC algorithm for block structural learning in Gaussian graphical models with a G-Wishart prior, enabling group-wise edge updates.

Findings

Effective in identifying block structures in graphs

Improves smoothing of functional data using graphical models

Provides a practical algorithm for group-based graph learning

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.