Polyhedral Aspects of Maxoids
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866918388520976384 |
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| author | Boege, Tobias Ferry, Kamillo Hollering, Benjamin Nowell, Francesco |
| author_facet | Boege, Tobias Ferry, Kamillo Hollering, Benjamin Nowell, Francesco |
| contents | The conditional independence (CI) relation of a distribution in a max-linear Bayesian network depends on its weight matrix through the $C^\ast$-separation criterion. These CI~models, which we call maxoids, are compositional graphoids which are in general not representable by Gaussian random variables. We prove that every maxoid can be obtained from a transitively closed weighted DAG and show that the stratification of generic weight matrices by their maxoids yields a polyhedral~fan. We also use this connection to polyhedral geometry to develop an algorithm for solving the conditional independence implication problem for maxoids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21068 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polyhedral Aspects of Maxoids Boege, Tobias Ferry, Kamillo Hollering, Benjamin Nowell, Francesco Combinatorics Statistics Theory 62R01, 14T90 (primary), 52C35 (secondary) The conditional independence (CI) relation of a distribution in a max-linear Bayesian network depends on its weight matrix through the $C^\ast$-separation criterion. These CI~models, which we call maxoids, are compositional graphoids which are in general not representable by Gaussian random variables. We prove that every maxoid can be obtained from a transitively closed weighted DAG and show that the stratification of generic weight matrices by their maxoids yields a polyhedral~fan. We also use this connection to polyhedral geometry to develop an algorithm for solving the conditional independence implication problem for maxoids. |
| title | Polyhedral Aspects of Maxoids |
| topic | Combinatorics Statistics Theory 62R01, 14T90 (primary), 52C35 (secondary) |
| url | https://arxiv.org/abs/2504.21068 |