Wasserstein Distance to Independence Models
Optimization and Control
2020-10-16 v2 Statistics Theory
Statistics Theory
Abstract
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.
Cite
@article{arxiv.2003.06725,
title = {Wasserstein Distance to Independence Models},
author = {Türkü Özlüm Çelik and Asgar Jamneshan and Guido Montúfar and Bernd Sturmfels and Lorenzo Venturello},
journal= {arXiv preprint arXiv:2003.06725},
year = {2020}
}