Wasserstein Distance to Independence Models
Bernd Sturmfels
An independence model for discrete random variables is a variety in a probability simplex. Given any data distribution, we seek to minimize the Wasserstein distance to the model. That distance comes from a polyhedral norm whose unit ball is dual to an alcoved polytope. The solution to our optimization problem is a piecewise algebraic function of the data. In this talk we discuss the combinatorial and geometric structure of this function.