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.

离散随机变量的独立性模型是概率单纯形中的Segre-Veronese变体。随机变量的联合状态集上的任何度量都将诱发概率单纯形上的Wasserstein度量。该多面体范数的单位球是Lipschitz多面体的对偶。给定任何数据分布，我们都试图将其Wasserstein距离最小化为固定的独立模型。该优化问题的解决方案是数据的分段代数函数。我们在很小的情况下显式地计算该函数，我们通常研究其组合结构和代数度，并提供一些实验案例研究。