Cross-Validated Causal Inference: a Modern Method to Combine Experimental and Observational Data

TL;DR

This paper introduces a modern method for causal inference that combines experimental and observational data using a cross-validated empirical risk minimization framework, improving estimation accuracy and reliability.

Contribution

It proposes a systematic framework that integrates experimental and observational data for causal estimation via ERM, with cross-validation for optimal weighting.

Findings

Effective integration of experimental and observational data demonstrated on real and synthetic datasets.

The method provides theoretical non-asymptotic error bounds.

Improved causal estimation accuracy and robustness.

Abstract

We develop new methods to integrate experimental and observational data in causal inference. While randomized controlled trials offer strong internal validity, they are often costly and therefore limited in sample size. Observational data, though cheaper and often with larger sample sizes, are prone to biases due to unmeasured confounders. To harness their complementary strengths, we propose a systematic framework that formulates causal estimation as an empirical risk minimization (ERM) problem. A full model containing the causal parameter is obtained by minimizing a weighted combination of experimental and observational losses--capturing the causal parameter's validity and the full model's fit, respectively. The weight is chosen through cross-validation on the causal parameter across experimental folds. Our experiments on real and synthetic data show the efficacy and reliability of our method. We also provide theoretical non-asymptotic error bounds.