Primary Submission Category: Causal Discovery
Post-selection inference for causal effects after causal discovery
Authors: Ting-Hsuan Chang, Zijian Guo, Daniel Malinsky,
Presenting Author: Ting-Hsuan Chang*
Algorithms for constraint-based causal discovery select graphical causal models from among a space of possible candidates (e.g., all directed acyclic graphs) by executing a sequence of conditional independence tests. These may be used to inform the estimation of causal effects (e.g., average treatment effects) when there is uncertainty about which covariates ought to be adjusted for, or which variables act as confounders versus mediators. However, naively using the data twice, for model selection and estimation, would lead to invalid confidence intervals. Moreover, if the selected graph is incorrect, the inferential claims may apply to a chosen functional that is distinct from the actual causal effect. We propose an approach to post-selection inference that is based on a resampling procedure, that essentially performs causal discovery multiple times with randomly varying intermediate test statistics. Then, an estimate of the target causal effect and corresponding confidence sets are constructed from a union of individual graph-based estimates and intervals. We show that this construction has asymptotically correct coverage. Though most of our exposition focuses on the PC algorithm for learning directed acyclic graphs and the multivariate Gaussian case for simplicity, the approach is general and modular, so it can be used with other conditional independence based discovery algorithms and (semi-)parametric families.