Exploration of the search space of Gaussian graphical models for paired data

• URL: http://arxiv.org/abs/2303.05561v2
• Date: Mon, 15 Apr 2024 14:43:05 GMT
• Title: Exploration of the search space of Gaussian graphical models for paired data
• Authors: Alberto Roverato, Dung Ngoc Nguyen,
• Abstract summary: We focus on a family of coloured Gaussian graphical models specifically suited for the paired data problem. We introduce a novel order between models, named the twin order. We show that, embedded with this order, the model space is a lattice that, unlike the model inclusion lattice, is distributive.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of learning a Gaussian graphical model in the case where the observations come from two dependent groups sharing the same variables. We focus on a family of coloured Gaussian graphical models specifically suited for the paired data problem. Commonly, graphical models are ordered by the submodel relationship so that the search space is a lattice, called the model inclusion lattice. We introduce a novel order between models, named the twin order. We show that, embedded with this order, the model space is a lattice that, unlike the model inclusion lattice, is distributive. Furthermore, we provide the relevant rules for the computation of the neighbours of a model. The latter are more efficient than the same operations in the model inclusion lattice, and are then exploited to achieve a more efficient exploration of the search space. These results can be applied to improve the efficiency of both greedy and Bayesian model search procedures. Here we implement a stepwise backward elimination procedure and evaluate its performance by means of simulations. Finally, the procedure is applied to learn a brain network from fMRI data where the two groups correspond to the left and right hemispheres, respectively.

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