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arXiv · 2206.14274

Learning block structured graphs in Gaussian graphical models

Alessandro Colombi·Raffaele Argiento·Lucia Paci·Alessia Pini
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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.

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Alessandro Colombi, Raffaele Argiento, Lucia Paci, Alessia Pini. 2022-06-28. Learning block structured graphs in Gaussian graphical models. https://doi.org/10.1080/10618600.2023.2210184

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