论文标题
因果图形模型中有效的最低成本调整集的注释
A note on efficient minimum cost adjustment sets in causal graphical models
论文作者
论文摘要
我们研究了根据个性化治疗规则估算介入平均值的调整集选择。我们假设一个非参数因果图形模型，可能是隐藏变量，至少一个由可观察变量组成的调整集。此外，我们假设可观察到的变量具有与之相关的正成本。我们将可观察到的调整集的成本定义为构成该变量的成本的总和。我们表明，在这种情况下，存在最低成本最佳的调整集，因为它们产生了介入平均值的非参数估计量，而在控制可观察到的具有最低成本的可观察到的调整集中的渐近方差中，其渐近方差最小。我们的结果基于与原始因果图相关的特殊流网络的构建。我们表明，可以通过计算网络上的最大流量，然后通过增强路径来找到可从源到达的顶点来找到最低成本最佳调整集。 OptimalAdj Python软件包实现了本文介绍的算法。
We study the selection of adjustment sets for estimating the interventional mean under an individualized treatment rule. We assume a non-parametric causal graphical model with, possibly, hidden variables and at least one adjustment set comprised of observable variables. Moreover, we assume that observable variables have positive costs associated with them. We define the cost of an observable adjustment set as the sum of the costs of the variables that comprise it. We show that in this setting there exist adjustment sets that are minimum cost optimal, in the sense that they yield non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that control for observable adjustment sets that have minimum cost. Our results are based on the construction of a special flow network associated with the original causal graph. We show that a minimum cost optimal adjustment set can be found by computing a maximum flow on the network, and then finding the set of vertices that are reachable from the source by augmenting paths. The optimaladj Python package implements the algorithms introduced in this paper.
