Lawrence Lifts, Matroids, and Maximum Likelihood Degrees
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911298159116288 |
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| author | Brysiewicz, Taylor Maraj, Aida |
| author_facet | Brysiewicz, Taylor Maraj, Aida |
| contents | We express the maximum likelihood (ML) degrees of a family toric varieties in terms of Mobius invariants of matroids. The family of interest are those parametrized by monomial maps given by Lawrence lifts of totally unimodular matrices with even circuits. Specifying these matrices to be vertex-edge incidence matrices of bipartite graphs gives the ML degrees of some hierarchical models and three dimensional quasi-independence models. Included in this list are the no-three-way interaction models with one binary random variable, for which, we give closed formulae. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_13064 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lawrence Lifts, Matroids, and Maximum Likelihood Degrees Brysiewicz, Taylor Maraj, Aida Combinatorics Algebraic Geometry 62R01 (Primary) 52B40, 14M25 (Secondary) We express the maximum likelihood (ML) degrees of a family toric varieties in terms of Mobius invariants of matroids. The family of interest are those parametrized by monomial maps given by Lawrence lifts of totally unimodular matrices with even circuits. Specifying these matrices to be vertex-edge incidence matrices of bipartite graphs gives the ML degrees of some hierarchical models and three dimensional quasi-independence models. Included in this list are the no-three-way interaction models with one binary random variable, for which, we give closed formulae. |
| title | Lawrence Lifts, Matroids, and Maximum Likelihood Degrees |
| topic | Combinatorics Algebraic Geometry 62R01 (Primary) 52B40, 14M25 (Secondary) |
| url | https://arxiv.org/abs/2310.13064 |