Andrew, B., Westhead, D.R. orcid.org/0000-0002-0519-3820 and Cutillo, L. orcid.org/0000-0002-2205-0338 (2025) Gaussian Graphical Modelling Without Independence Assumptions for Uncentered Data. In: Proceedings of the AAAI Conference on Artificial Intelligence. Thirty-Ninth AAAI Conference on Artificial Intelligence, 25 Feb - 04 Mar 2025, Philadelphia, USA. Association for the Advancement of Artificial Intelligence (AAAI) , pp. 15391-15398.
Abstract
The independence assumption between random variables is a useful tool to increase the tractability of a modelling framework. However, this assumption can be too simplistic; failing to take dependencies into account can cause models to fail dramatically. The field of multi-axis graphical modelling (also called multi-way modelling, Kronecker-separable modelling) has seen growth over the past decade, but these models require that the data have zero mean. In the multi-axis case, inference is typically done in the single sample scenario, making mean inference impossible. In this paper, we demonstrate how the zero-mean assumption can cause egregious modelling errors for Kronecker-sum-decomposable Gaussian graphical models, as well as propose a relaxation to the zero-mean assumption that allows the avoidance of such errors. Specifically, we propose the "Kronecker-sum-structured mean" assumption, which leads to models with nonconvex-but-unimodal log-likelihoods that can be solved efficiently with coordinate descent.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) The University of Leeds > Faculty of Biological Sciences (Leeds) > School of Molecular and Cellular Biology (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 28 May 2025 11:48 |
Last Modified: | 28 May 2025 11:48 |
Status: | Published |
Publisher: | Association for the Advancement of Artificial Intelligence (AAAI) |
Identification Number: | 10.1609/aaai.v39i15.33689 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:227094 |