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.
Keywords
toric variety, maximum likelihood degree, Lawrence lift,
matroid, algebraic statistics
