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

arXiv: https://arxiv.org/abs/2511.00727 · HTML: https://mlsanity.com/paper/2511.00727/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2025.

## Built on by (most cited first, 2 of 2)

- [The Partial Testimony of Logs: Evaluation of Language Model Generation under Confounded Model Choice](https://mlsanity.com/paper/2605.01311/) (2026)
- [Testing Effect Homogeneity and Confounding in High-Dimensional Experimental and Observational Studies](https://mlsanity.com/paper/2602.19703/) (2026)

## Abstract (arXiv)

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.