Gaussian Graphical Modelling Without Independence Assumptions for Uncentered Data
Bailey Andrew, David R. Westhead, Luisa Cutillo
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.
BibTeX
@article{Andrew_Westhead_Cutillo_2025, title={Gaussian Graphical Modelling Without Independence Assumptions for Uncentered Data}, volume={39}, url={https://ojs.aaai.org/index.php/AAAI/article/view/33689}, DOI={10.1609/aaai.v39i15.33689}, abstractNote={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.}, number={15}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Andrew, Bailey and Westhead, David R. and Cutillo, Luisa}, year={2025}, month={Apr.}, pages={15391-15398} }