Primary Submission Category: Machine Learning and Causal Inference
Stable Causal Estimation with Transport Maps
Authors: Yidan Xu, Yixin Wang, Long Nguyen,
Presenting Author: Yidan Xu*
This paper develops a causal estimation framework with Optimal Transport (OT) map for observational studies. Importance weighting based adjustment is known to have high sampling variance under lack of strong overlap, which could happen under high dimensional covariate space or small sample size. On the other hand, OT map proves to be a more stable method for tackling distribution shift, which can be applied to discrete distribution and is able to accommodate various data types.
Given these advantages, we propose a framework for causal estimation with OT map under superpopulation setting. With a binary treatment regime, we provide identifiability conditions and propose estimators for average treatment effects. To accommodate lack of overlap conditions, we extend the methodology with linear interpolation maps between treatment and control covariate distributions. Across different choices of distribution discrepancy and user selected upper bound, we demonstrate that the bias owing to lack of overlap can be reduced under outcome regression model misspecification.