Exploration of the search space of Gaussian graphical models for paired data
This work addresses the challenge of modeling dependent groups in statistical learning, with applications in fields like neuroscience, though it appears incremental as it builds on existing graphical model frameworks.
The authors tackled the problem of learning Gaussian graphical models for paired data by introducing a novel twin order that makes the model space a distributive lattice, enabling more efficient search space exploration. They implemented a stepwise backward elimination procedure, applied it to fMRI brain network data, and evaluated performance through simulations.
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.