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
-determinant and
its ML degree. Similarly, for models defined by the second hypersimplex, we determine its principal
-determinant
and give computational evidence towards a conjectured lower bound of its ML
degree.
Keywords
maximum likelihood estimation, ML degrees, matroids