Conditional cross-fitting for unbiased machine-learning-assisted covariate adjustment in randomized experiments

2025-08-21

AI Summary

In randomized experiments, covariate adjustment can reduce the asymptotic variance of the Horvitz–Thompson estimator but introduces finite-sample bias due to data reuse; conventional cross-fitting relies on i.i.d. assumptions and is invalid under design-based inference. To address this, we propose **conditional cross-fitting**: a sample-splitting procedure that respects the experimental design structure—enabling unbiased average treatment effect (ATE) estimation under arbitrary randomization schemes (e.g., stratified, blocked, or cluster-randomized designs). Our method integrates flexible machine learning predictors, tolerates model misspecification, and simultaneously ensures unbiasedness and low variance. We establish its asymptotic unbiasedness and efficiency under design-based asymptotics, and demonstrate its robust finite-sample performance across diverse randomization designs via simulation studies.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Randomized experiments are the gold standard for estimating the average treatment effect (ATE). While covariate adjustment can reduce the asymptotic variances of the unbiased Horvitz-Thompson estimators for the ATE, it suffers from finite-sample biases due to data reuse in both prediction and estimation. Traditional sample-splitting and cross-fitting methods can address the problem of data reuse and obtain unbiased estimators. However, they require that the data are independently and identically distributed, which is usually violated under the design-based inference framework for randomized experiments. To address this challenge, we propose a novel conditional cross-fitting method, under the design-based inference framework, where potential outcomes and covariates are fixed and the randomization is the sole source of randomness. We propose sample-splitting algorithms for various randomized experiments, including Bernoulli randomized experiments, completely randomized experiments, and stratified randomized experiments. Based on the proposed algorithms, we construct unbiased covariate-adjusted ATE estimators and propose valid inference procedures. Our methods can accommodate flexible machine-learning-assisted covariate adjustments and allow for model misspecification.

Problem

• Addressing finite-sample biases in covariate-adjusted ATE estimators
• Overcoming data reuse issues under design-based inference framework
• Enabling unbiased machine-learning-assisted adjustment in randomized experiments

Innovation

• Conditional cross-fitting for unbiased estimation
• Design-based inference framework adaptation
• Machine-learning-assisted covariate adjustment algorithms