Lawrence lifts, matroids, and maximum likelihood degrees
Copyright policy )Lawrence lifts, matroids, and maximum likelihood degrees
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.
23 pages, 5 figures. Comments welcome!
- Western University Canada
- Regents of the University of Michigan - Ann Arbor United States
- University of Michigan–Flint United States
- University of Chicago United States
62R01 (Primary) 52B40, 14M25 (Secondary), Combinatorics, FOS: Mathematics, Combinatorics (math.CO), Algebraic Geometry, Algebraic Geometry (math.AG)
62R01 (Primary) 52B40, 14M25 (Secondary), Combinatorics, FOS: Mathematics, Combinatorics (math.CO), Algebraic Geometry, Algebraic Geometry (math.AG)
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