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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Online Access: | https://arxiv.org/abs/2303.05561 |
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| _version_ | 1866909170019598336 |
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| author | Roverato, Alberto Nguyen, Dung Ngoc |
| author_facet | Roverato, Alberto Nguyen, Dung Ngoc |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_05561 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exploration of the search space of Gaussian graphical models for paired data Roverato, Alberto Nguyen, Dung Ngoc Machine Learning Neurons and Cognition Methodology 62A06 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. |
| title | Exploration of the search space of Gaussian graphical models for paired data |
| topic | Machine Learning Neurons and Cognition Methodology 62A06 |
| url | https://arxiv.org/abs/2303.05561 |