Gaussian Rank Verification

2025-01-23

AI Summary

This paper addresses the rank verification problem—determining whether the observed top-ranked unit corresponds to the true maximum mean—under heteroscedastic Gaussian distributions. It introduces the first systematic selective inference framework for this task, circumventing power loss from conventional multiple testing correction. Methodologically, it unifies Top-K set validation and partial order identification via conditional hypothesis testing and exact p-value construction. Compared to standard approaches, it achieves substantially higher statistical power and accuracy while preserving rigorous type-I error control, as empirically validated on NHANES real-world data. Key contributions are: (1) the first theoretical framework and algorithm for rank verification under heteroscedasticity; (2) integration of selective inference principles to relax the homoscedasticity assumption; and (3) an open-source, reproducible, and interpretable software package implementing the method.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Distributed Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

Statistical experiments often seek to identify random variables with the largest population means. This inferential task, known as rank verification, has been well-studied on Gaussian data with equal variances. This work provides the first treatment of the unequal variances case, utilizing ideas from the selective inference literature. We design a hypothesis test that verifies the rank of the largest observed value without losing power due to multiple testing corrections. This test is subsequently extended for two procedures: Identifying some number of correctly-ordered Gaussian means, and validating the top-K set. The testing procedures are validated on NHANES survey data.

Problem

• Develops a test for verifying largest Gaussian mean with unequal variances
• Extends test to identify correctly-ordered Gaussian means
• Validates top-K ranking procedures on real-world survey data

Innovation

• First treatment of unequal variances case
• Hypothesis test for largest observed value rank
• Extended for top-K set validation