Generalization Bounds for Causal Regression: Insights, Guarantees and Sensitivity Analysis

TL;DR

This paper develops a theoretical framework with generalization bounds for causal regression algorithms, providing guarantees even with hidden confounding and limited data, and demonstrates their practical tightness.

Contribution

It introduces a novel change-of-measure inequality to tightly bound causal model loss based on treatment propensity deviations, extending guarantees to complex causal scenarios.

Findings

Bounds are empirically tight on real and semi-synthetic data.

Guarantees hold despite hidden confounding and positivity violations.

Theoretical insights improve understanding of causal algorithm generalization.

Abstract

Many algorithms have been recently proposed for causal machine learning. Yet, there is little to no theory on their quality, especially considering finite samples. In this work, we propose a theory based on generalization bounds that provides such guarantees. By introducing a novel change-of-measure inequality, we are able to tightly bound the model loss in terms of the deviation of the treatment propensities over the population, which we show can be empirically limited. Our theory is fully rigorous and holds even in the face of hidden confounding and violations of positivity. We demonstrate our bounds on semi-synthetic and real data, showcasing their remarkable tightness and practical utility.