论文标题

具有隐藏变量的因果图形模型中的有效调整集

Efficient adjustment sets in causal graphical models with hidden variables

论文作者

Smucler, Ezequiel, Sapienza, Facundo, Rotnitzky, Andrea

论文摘要

我们研究了协变量调整集的选择,以估计点暴露动态策略的价值,也称为动态治疗方案,假设具有隐藏变量的非参数因果图形模型,其中至少可以完全观察到一个调整集。我们表明,最近开发的标准(对于没有隐藏变量的图形)来比较控制某些调整集的静态策略值的非参数估计值的渐近方差,在动态策略和图形和隐藏变量下也是有效的。我们表明,存在最佳最小(最小值)的调整集,这是在控制最小的调整集(最小基数)的调整集中的估计器的意义上。此外,我们表明,如果没有隐藏变量,或者所有可观察到的变量都是治疗,结果或用于决定治疗的变量的祖先,则存在全球最佳调整集。我们提供多项式时间算法来计算全球最佳(存在),最佳最小和最佳最小调节集。我们的结果基于一个无向图的构造,在该图中,在处理和结果变量之间切换对应于调整集。在此无方向的图中,可以定义最小顶点切割之间的部分顺序,从而使最小切割的一组晶格成为晶格。该部分顺序直接对应于相应非参数调整估计量的渐近方差的顺序。

We study the selection of covariate adjustment sets for estimating the value of point exposure dynamic policies, also known as dynamic treatment regimes, assuming a non-parametric causal graphical model with hidden variables, in which at least one adjustment set is fully observable. We show that recently developed criteria, for graphs without hidden variables, to compare the asymptotic variance of non-parametric estimators of static policy values that control for certain adjustment sets, are also valid under dynamic policies and graphs with hidden variables. We show that there exist adjustment sets that are optimal minimal (minimum), in the sense of yielding estimators with the smallest variance among those that control for adjustment sets that are minimal (of minimum cardinality). Moreover, we show that if either no variables are hidden or if all the observable variables are ancestors of either treatment, outcome, or the variables that are used to decide treatment, a globally optimal adjustment set exists. We provide polynomial time algorithms to compute the globally optimal (when it exists), optimal minimal, and optimal minimum adjustment sets. Our results are based on the construction of an undirected graph in which vertex cuts between the treatment and outcome variables correspond to adjustment sets. In this undirected graph, a partial order between minimal vertex cuts can be defined that makes the set of minimal cuts a lattice. This partial order corresponds directly to the ordering of the asymptotic variances of the corresponding non-parametrically adjusted estimators.

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