Tropical combinatorics of max-linear Bayesian networks
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912647388069888 |
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| author | Améndola, Carlos Ferry, Kamillo |
| author_facet | Améndola, Carlos Ferry, Kamillo |
| contents | A polytrope is a tropical polyhedron that is also classically convex. We study the tropical combinatorial types of polytropes associated to weighted directed acyclic graphs (DAGs). This family of polytropes arises in algebraic statistics when describing the model class of max-linear Bayesian networks. We show how the edge weights of a network directly relate to the facet structure of the corresponding polytrope. We also give a classification of polytropes from weighted DAGs at different levels of equivalence. These results give insight on the statistical problem of identifiability for a max-linear Bayesian network. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_10394 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tropical combinatorics of max-linear Bayesian networks Améndola, Carlos Ferry, Kamillo Combinatorics Algebraic Geometry Statistics Theory 05C12, 14T90, 52B11, 62R01 A polytrope is a tropical polyhedron that is also classically convex. We study the tropical combinatorial types of polytropes associated to weighted directed acyclic graphs (DAGs). This family of polytropes arises in algebraic statistics when describing the model class of max-linear Bayesian networks. We show how the edge weights of a network directly relate to the facet structure of the corresponding polytrope. We also give a classification of polytropes from weighted DAGs at different levels of equivalence. These results give insight on the statistical problem of identifiability for a max-linear Bayesian network. |
| title | Tropical combinatorics of max-linear Bayesian networks |
| topic | Combinatorics Algebraic Geometry Statistics Theory 05C12, 14T90, 52B11, 62R01 |
| url | https://arxiv.org/abs/2411.10394 |