Graphical Modelling without Independence Assumptions for Uncentered Data
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.02393
- arXiv:
- arXiv:2408.02393
- Bibcode:
- 2024arXiv240802393A
- Keywords:
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- Statistics - Methodology;
- Statistics - Machine Learning
- E-Print:
- 7 pages (13 counting refs &