PAC Style Guarantees for Doubly Robust Generalized Front-Door Estimator

Yuhao Wang, Arnab Bhattacharyya, Jin Tian, N. V. Vinodchandran

Keywords: causal inference, PAC style guarantees, front door, back door, doubly robust

Abstract: Doubly robust estimators present a promising methodology for estimating treatment effects in observational studies. This paper provides a finite sample analysis of the doubly robust estimators for both the back-door model (where treatment, outcome, and covariates are observed) and the generalized front-door model (which includes unmeasured confounding). Our approach establishes PAC-style guarantees of the deviation of the estimators in term of the divergence of probability distributions. These bounds demonstrate that minimizing the estimation error of the treatment effect in terms of Chi-square distance is crucial for minimizing the variance between true and estimated model.

Submission Number: 17