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Lawrence lifts,
matroids, and maximum likelihood degrees
Taylor Brysiewicz and Aida Maraj |
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Vol. 16 (2025), No. 2, 217–242
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Abstract |
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We express the maximum likelihood (ML) degrees of a family of toric varieties in terms of Möbius 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. |
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Keywords
toric variety, maximum likelihood degree, Lawrence lift,
matroid, algebraic statistics
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Mathematical Subject Classification
Primary: 14M25, 52B40, 62R01
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Milestones
Received: 15 January 2025
Revised: 4 November 2025
Accepted: 5 November 2025
Published: 28 November 2025
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Authors |
| Taylor Brysiewicz | |
| Department of Mathematics University of Western Ontario London, ON Canada |
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| Aida Maraj | |
| Department of Mathematics University of Michigan Ann Arbor, MI United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
