  An independence model for discrete random variables is a Segre-Veronese
variety in a probability simplex. Any metric on the set of joint states of the
random variables induces a Wasserstein metric on the probability simplex. The
unit ball of this polyhedral norm is dual to the Lipschitz polytope. Given any
data distribution, we seek to minimize its Wasserstein distance to a fixed
independence model. The solution to this optimization problem is a piecewise
algebraic function of the data. We compute this function explicitly in small
instances, we examine its combinatorial structure and algebraic degrees in the
general case, and we present some experimental case studies.
