Hypergraph Variable Selection with False Discovery Rate Control

2026-06-18

AI Summary

This work addresses the challenge of variable selection in the presence of complex dependency structures among predictors, where conventional methods struggle to simultaneously achieve high statistical power and rigorous control of the false discovery rate (FDR). The authors propose a hypergraph-based variable selection framework that constructs set hypotheses over overlapping groups of variables and introduces a generalized FDR definition tailored to such structured dependencies. By integrating hypergraph modeling, an extension of hierarchical clustering, and set-based hypothesis testing, the method substantially enhances selection power across diverse dependency scenarios while maintaining strict FDR control. The key innovation lies in the incorporation of hypergraph structures into variable selection and the development of a corresponding theoretical foundation for generalized FDR guarantees.

Abstract

Variable selection methods that control the false discovery rate often lose power when predictors exhibit complex dependence structures. We previously showed that selecting hierarchically clustered groups of predictors can mitigate this issue while maintaining false discovery rate control. When correlations are less structured, however, overlapping predictor sets may be more effective. We introduce a generalized false discovery rate for hypotheses defined on sets of predictors and propose a hypergraph-based selection method. This approach achieves higher power across diverse settings while preserving rigorous false discovery rate control.

Problem

• variable selection
• false discovery rate
• complex dependence
• hypergraph
• predictor sets

Innovation

• hypergraph
• false discovery rate
• variable selection
• overlapping groups
• generalized FDR