论文标题
切向沃斯堡的预测
Tangential Wasserstein Projections
论文作者
论文摘要
我们使用2-wasserstein空间的几何特性在一组概率度量之间提出了一个投影概念。它是为一般的多元概率度量而设计的，在计算上有效地实现，并在常规设置中提供了独特的解决方案。这个想法是使用广义的大地测量学处理瓦斯汀空间的常规切线锥。它的结构和计算属性使该方法适用于各种设置，从因果推断到对象数据的分析。估计因果效应的应用将合成控制的概念概括为具有个体级异质性的多元数据，以及一种在所有时间段内共同估计最佳权重的方法。
We develop a notion of projections between sets of probability measures using the geometric properties of the 2-Wasserstein space. It is designed for general multivariate probability measures, is computationally efficient to implement, and provides a unique solution in regular settings. The idea is to work on regular tangent cones of the Wasserstein space using generalized geodesics. Its structure and computational properties make the method applicable in a variety of settings, from causal inference to the analysis of object data. An application to estimating causal effects yields a generalization of the notion of synthetic controls to multivariate data with individual-level heterogeneity, as well as a way to estimate optimal weights jointly over all time periods.
