Matroid Stratification of ML Degrees of Independence Models
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866915046195462144 |
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| author | Clarke, Oliver Hoşten, Serkan Kushnerchuk, Nataliia Oldekop, Janike |
| author_facet | Clarke, Oliver Hoşten, Serkan Kushnerchuk, Nataliia Oldekop, Janike |
| contents | We study the maximum likelihood (ML) degree of discrete exponential independence models and models defined by the second hypersimplex. For models with two independent variables, we show that the ML degree is an invariant of a matroid associated to the model. We use this description to explore ML degrees via hyperplane arrangements. For independence models with more variables, we investigate the connection between the vanishing of factors of its principal $A$-determinant and its ML degree. Similarly, for models defined by the second hypersimplex, we determine its principal $A$-determinant and give computational evidence towards a conjectured lower bound of its ML degree. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_10010 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Matroid Stratification of ML Degrees of Independence Models Clarke, Oliver Hoşten, Serkan Kushnerchuk, Nataliia Oldekop, Janike Statistics Theory Algebraic Geometry Combinatorics 62R01 (Primary) 14M25, 13P15, 05B35, 62F10 (Secondary) We study the maximum likelihood (ML) degree of discrete exponential independence models and models defined by the second hypersimplex. For models with two independent variables, we show that the ML degree is an invariant of a matroid associated to the model. We use this description to explore ML degrees via hyperplane arrangements. For independence models with more variables, we investigate the connection between the vanishing of factors of its principal $A$-determinant and its ML degree. Similarly, for models defined by the second hypersimplex, we determine its principal $A$-determinant and give computational evidence towards a conjectured lower bound of its ML degree. |
| title | Matroid Stratification of ML Degrees of Independence Models |
| topic | Statistics Theory Algebraic Geometry Combinatorics 62R01 (Primary) 14M25, 13P15, 05B35, 62F10 (Secondary) |
| url | https://arxiv.org/abs/2312.10010 |