A0631
Title: Inference for individual mediation effects and interventional effects in sparse high-dimensional causal graphical models
Authors: Abhishek Chakrabortty - Texas A\&M University (United States) [presenting]
Abstract: The problem of identifying mediators that regulate the effect of a treatment on a response variable is considered. While there has been significant work on this classical topic, little work has been done when the set of potential mediators is high-dimensional (HD). A further complication arises when they are interrelated with unknown dependencies. We assume that the causal structure of the treatment, confounders, potential mediators and the response is an (unknown) directed acyclic graph (DAG). HD DAG models have previously been used to estimate causal effects from observational data, and methods called IDA and joint-IDA have been developed to estimate the effects of single and multiple interventions. Here we propose an IDA-type method called MIDA for estimating so-called individual mediation effects from HD observational data. Although IDA and joint-IDA estimators have been shown to be consistent in certain sparse HD settings, their asymptotic properties, such as convergence in distribution and inferential tools in such settings, have stayed unknown. We prove the HD consistency of MIDA for linear structural equation models with sub-Gaussian errors. More importantly, we derive distributional convergence results for MIDA in similar HD settings, which apply to IDA and joint-IDA estimators as well. To our knowledge, these are the first such distributional convergence results facilitating inference for IDA-type estimators. We also validate our results via numerical studies.
