Generalization Bounds for Causal Regression: Insights, Guarantees and Sensitivity Analysis
This work provides rigorous theoretical foundations for causal regression, addressing a critical gap for researchers and practitioners in causal machine learning, though it is incremental in building on existing generalization theory.
The authors tackled the lack of theoretical guarantees for causal machine learning algorithms by proposing generalization bounds based on a novel change-of-measure inequality, which tightly bounds model loss in terms of treatment propensity deviations and works under hidden confounding and positivity violations, demonstrating tightness and utility on semi-synthetic and real data.
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.