Graphical Modelling without Independence Assumptions for Uncentered Data
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911977349054464 |
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| author | Andrew, Bailey Westhead, David R. Cutillo, Luisa |
| author_facet | Andrew, Bailey Westhead, David R. Cutillo, Luisa |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02393 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graphical Modelling without Independence Assumptions for Uncentered Data Andrew, Bailey Westhead, David R. Cutillo, Luisa Methodology Machine Learning 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. |
| title | Graphical Modelling without Independence Assumptions for Uncentered Data |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2408.02393 |