论文标题
Wasserstein距离独立模型的距离
Wasserstein Distance to Independence Models
论文作者
论文摘要
离散随机变量的独立模型是概率单纯性中的Segre-veronese品种。随机变量的关节状态集上的任何度量都会在概率单纯性上引起wasserstein度量。该多面体标准的单位球对Lipschitz polytope是双重的。鉴于任何数据分布，我们试图最大程度地减少其与固定独立模型的遗嘱距离。解决此优化问题的解决方案是数据的分段代数函数。我们在小实例中明确计算此功能，在一般情况下检查其组合结构和代数度，并提出一些实验案例研究。
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.
