The Unified Non-Convex Framework for Robust Causal Inference: Overcoming the Gaussian Barrier and Optimization Fragility

TL;DR

The paper addresses the fragility of traditional convex causal estimators under high-dimensional nuisance parameters and data contamination, proposing a Unified Robust Framework for estimating the Average Treatment Effect on the Overlap (ATO). It combines gamma-divergence (density power divergence) with an analytic bias correction to restore double robustness, uses Graduated Non-Convexity (GNC) to navigate non-convex optimization, and employs an Adaptive Gatekeeper to respect the Gaussian Barrier while selecting appropriate orthogonality order. Nuisance estimation is handled via Gamma-Lasso with a one-step estimator path to achieve diminishing bias and an Oracle Property, while the Gatekeeper adapts the estimation strategy to the residual distribution (Gaussian vs non-Gaussian). Collectively, this framework enhances robustness to outliers and lack of overlap, provides tractable optimization, and offers practical deployment benefits for policy-relevant causal inference in modern data environments.

Abstract

This document proposes a Unified Robust Framework that re-engineers the estimation of the Average Treatment Effect on the Overlap (ATO). It synthesizes gamma-Divergence for outlier robustness, Graduated Non-Convexity (GNC) for global optimization, and a "Gatekeeper" mechanism to address the impossibility of higher-order orthogonality in Gaussian regimes.