False Discovery Rate Control via Bayesian Mirror Statistic

2025-10-01

AI Summary

Addressing challenges in high-dimensional variable selection—including stringent false discovery rate (FDR) control and efficiency loss from data splitting—this paper introduces the first Bayesian mirror statistic framework. Instead of partitioning data, it directly constructs mirror statistics from the posterior distribution of regression coefficients within a unified Bayesian model. The approach accommodates both continuous and discrete responses, as well as complex models (e.g., mixed-effects models), leveraging automatic differentiation variational inference (ADVI) with continuous priors for scalable and accurate posterior approximation. Theoretically, it guarantees strict FDR control under mild regularity conditions. Empirically, it achieves superior statistical power and robust false positive control in high-dimensional settings. The core contribution is the development of a principled, flexible, and extensible Bayesian mirror statistic paradigm—unifying rigorous FDR control, modeling adaptability, and computational tractability.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Simultaneously performing variable selection and inference in high-dimensional models is an open challenge in statistics and machine learning. The increasing availability of vast amounts of variables requires the adoption of specific statistical procedures to accurately select the most important predictors in a high-dimensional space, while being able to control some form of selection error. In this work we adapt the Mirror Statistic approach to False Discovery Rate (FDR) control into a Bayesian modelling framework. The Mirror Statistic, developed in the classic frequentist statistical framework, is a flexible method to control FDR, which only requires mild model assumptions, but requires two sets of independent regression coefficient estimates, usually obtained after splitting the original dataset. Here we propose to rely on a Bayesian formulation of the model and use the posterior distributions of the coefficients of interest to build the Mirror Statistic and effectively control the FDR without the need to split the data. Moreover, the method is very flexible since it can be used with continuous and discrete outcomes and more complex predictors, such as with mixed models. We keep the approach scalable to high-dimensions by relying on Automatic Differentiation Variational Inference and fully continuous prior choices.

Problem

• Controls false discovery rate in high-dimensional variable selection
• Adapts frequentist mirror statistic to Bayesian modeling framework
• Eliminates data splitting requirement using posterior distributions

Innovation

• Bayesian Mirror Statistic for FDR control
• Uses posterior distributions without data splitting
• Scalable via variational inference with continuous priors