Flexible Inference for Winners with Conditional Validity

2026-07-20

AI Summary

This work addresses the pervasive winner’s curse in data-driven selection, wherein post-selection effect sizes—such as those of optimal treatments, models, or features—are systematically overestimated. The authors propose a novel method that integrates adaptive exponential randomization with conditional inference to correct selection-induced bias in a nonparametric setting. By embedding an adaptive randomization mechanism within the conditional inference framework, the approach achieves substantially shorter confidence intervals while preserving selection quality comparable to standard top-k procedures. Demonstrated across diverse applications—including clinical treatment evaluation, model leaderboard inference, and feature importance analysis—the method effectively mitigates the winner’s curse, yielding tighter and more reliable statistical inference.

Abstract

Researchers often select top-performing options or winners, based on a data-driven criterion, such as treatments, models, or model features and then report effect estimates for the selected winners. Naive post-selection estimates, however, are known to suffer from the winner's curse, producing systematically overoptimistic results. We introduce a flexible conditional inference method that corrects for this overoptimism through an adaptive exponential randomization scheme. Our method achieves selection quality that closely matches that of standard top-k selection, while also yielding shorter confidence intervals than existing approaches. Furthermore, our approach applies broadly to nonparametric settings with asymptotically linear selection statistics, covering wide-ranging applications such as inference for the efficacy of the most promising treatments in clinical trials, the abilities of top-ranked models on leaderboards, and the importance of the most predictive features in a model.

Problem

• winner's curse
• post-selection inference
• top-k selection
• overoptimistic estimation
• conditional validity

Innovation

• conditional inference
• winner's curse
• adaptive exponential randomization
• post-selection inference
• asymptotically linear statistics