Inference conditional on selection: a review

2026-04-10

AI Summary

Traditional statistical inference often fails when models or parameters are selected in a data-driven manner. This work systematically investigates selective inference, focusing on a conditional inference framework that conditions on the selection event to restore the nominal coverage of confidence intervals. We clarify the scientific interpretation of this framework, unify several existing approaches under its umbrella, and demonstrate its application to canonical settings such as inference for the “winner,” region-specific means in regression trees, and differences between clusters. Through simulations and analyses of single-cell RNA sequencing data, we show that the proposed methodology yields valid and reliable statistical inference in practical scenarios.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Calibration & Uncertainty Quantification
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

In this article, we review selective inference, a set of techniques for inference when the statistical question asked is a function of the data. This setting often arises in contemporary scientific workflows, where hypotheses and parameters may be selected from the data, rather than specified in advance. In this setting, classical inferential techniques do not achieve"classical"guarantees, such as nominal coverage of confidence intervals. We consider three examples for which selective inference solutions are required: inference on a"winner", inference on the mean of a region in a regression tree, and inference on the difference in means between a pair of clusters. We argue that conditional guarantees are of scientific interest in such settings. We then review and draw connections between several approaches that provide such guarantees. Finally, we illustrate these approaches in simulation and through an application to single-cell RNA sequencing data.

Problem

• selective inference
• data-driven selection
• conditional inference
• post-selection inference
• statistical guarantees

Innovation

• selective inference
• conditional inference
• data-driven hypotheses
• post-selection inference
• statistical guarantees