Home Page




Editorial Board

Special Issues

Open Source Software

Proceedings (PMLR)

Data (DMLR)

Transactions (TMLR)




Frequently Asked Questions

Contact Us

RSS Feed

Exploration of the Search Space of Gaussian Graphical Models for Paired Data

Alberto Roverato, Dung Ngoc Nguyen; 25(92):1−41, 2024.


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 both on synthetic and real-world data.

© JMLR 2024. (edit, beta)