Graphical Modelling without Independence Assumptions for Uncentered Data

• URL: http://arxiv.org/abs/2408.02393v1
• Date: Mon, 5 Aug 2024 11:40:23 GMT
• Title: Graphical Modelling without Independence Assumptions for Uncentered Data
• Authors: Bailey Andrew, David R. Westhead, Luisa Cutillo,
• Abstract summary: We show how the zero-mean assumption can cause egregious errors in modelling. Specifically, we propose a relaxation of the zero-mean assumption that allows the avoidance of such errors.
• Score: 0.30723404270319693
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The independence assumption is a useful tool to increase the tractability of one's modelling framework. However, this assumption does not match reality; 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, 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.

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