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.
Cite
@article{arxiv.2206.14274,
title = {Learning block structured graphs in Gaussian graphical models},
author = {Alessandro Colombi and Raffaele Argiento and Lucia Paci and Alessia Pini},
journal= {arXiv preprint arXiv:2206.14274},
year = {2023}
}