论文标题
限制定理的熵最佳传输图和凹凸不平的发散
Limit Theorems for Entropic Optimal Transport Maps and the Sinkhorn Divergence
论文作者
论文摘要
我们研究限制熵最佳运输（EOT）图，双重电位和凹痕差异的定理。我们使用的关键技术工具是对边际分布的EOT电位的一阶和二阶可不同性分析，这可能是独立的。鉴于可不同的结果，使用功能增量方法来获得用于经验EOT电位和地图的中心极限定理。利用了二阶功能增量方法来确定零下经验沉积物差异的极限分布。在后一个结果的基础上，我们进一步得出了sindhorn独立测试统计量的无限制分布，并表征了正确的顺序。由于我们的限制定理来自相关图的Hadamard可不同性，因此作为副产品，我们还获得了经验EOT图，电位和sindhorn差异的自举一致性和渐近效率。
We study limit theorems for entropic optimal transport (EOT) maps, dual potentials, and the Sinkhorn divergence. The key technical tool we use is a first and second-order Hadamard differentiability analysis of EOT potentials with respect to the marginal distributions, which may be of independent interest. Given the differentiability results, the functional delta method is used to obtain central limit theorems for empirical EOT potentials and maps. The second-order functional delta method is leveraged to establish the limit distribution of the empirical Sinkhorn divergence under the null. Building on the latter result, we further derive the null limit distribution of the Sinkhorn independence test statistic and characterize the correct order. Since our limit theorems follow from Hadamard differentiability of the relevant maps, as a byproduct, we also obtain bootstrap consistency and asymptotic efficiency of the empirical EOT map, potentials, and Sinkhorn divergence.
