Wasserstein distance to independence models. (May 2021)

• Record Type: Journal Article
• Authors: Çelik, Türkü Özlüm; Jamneshan, Asgar; Montúfar, Guido; Sturmfels, Bernd; Venturello, Lorenzo
• Is Part Of: Journal of symbolic computation. Volume 104(2021)
• Page Start: 855
• Page End: 873
• Publication Date: 2021-05
• Subjects: Algebraic statistics -- Lipschitz polytope -- Optimal transport -- Polar degrees -- Segre-Veronese variety -- Wasserstein distance; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.10.005
• Languages: English
• ISSNs: 0747-7171

Abstract

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 study its combinatorial structure and algebraic degrees in general, and we present some experimental case studies.