论文标题
定向最佳运输
The Directional Optimal Transport
论文作者
论文摘要
我们引入了一个约束的最佳运输问题，其中原始$ x $只能将其运输到目的地$ y \ geq x $。我们的统计动机是描述当效果单调或$ y \ geq x $时，给定边缘的治疗效果$ y-x $方差的尖锐上限。因此，我们专注于超模型成本（或子模型奖励），并引入一个耦合$ p _ {*} $，对于所有此类成本而言都是最佳的，并产生了急剧的界限。这种耦合允许多种表征 - 几何形状，订单理论，作为最佳运输，通过CDF以及通过传输内核解释其结构并暗示有用的界限。当第一个边缘是原子无原子时，$ p _ {*} $集中在两个地图的图上，可以用边缘来描述，这是由于结合约束而产生的第二张地图。
We introduce a constrained optimal transport problem where origins $x$ can only be transported to destinations $y\geq x$. Our statistical motivation is to describe the sharp upper bound for the variance of the treatment effect $Y-X$ given marginals when the effect is monotone, or $Y\geq X$. We thus focus on supermodular costs (or submodular rewards) and introduce a coupling $P_{*}$ that is optimal for all such costs and yields the sharp bound. This coupling admits manifold characterizations -- geometric, order-theoretic, as optimal transport, through the cdf, and via the transport kernel -- that explain its structure and imply useful bounds. When the first marginal is atomless, $P_{*}$ is concentrated on the graphs of two maps which can be described in terms of the marginals, the second map arising due to the binding constraint.
