Virtual Dummies: Enabling Scalable FDR-Controlled Variable Selection via Sequential Sampling of Null Features

TL;DR

This paper introduces Virtual Dummy LARS, a scalable method for FDR-controlled variable selection in high-dimensional genomics, reducing memory and computation while maintaining theoretical guarantees.

Contribution

It formalizes the information flow in dummy-based selection, deriving an adaptive sampling method that eliminates the need for large dummy matrices, enabling scalable FDR control.

Findings

VD-LARS reduces memory and runtime by several orders of magnitude.

The method preserves the exact FDR control and selection law of the original T-Rex selector.

Experiments show VD-T-Rex effectively controls FDR and maintains power in large-scale genome studies.

Abstract

High-dimensional variable selection, particularly in genomics, requires error-controlling procedures that scale to millions of predictors. The Terminating-Random Experiments (T-Rex) selector achieves false discovery rate (FDR) control by aggregating results of early terminated random experiments, each combining original predictors with i.i.d. synthetic null variables (dummies). At biobank scales, however, explicit dummy augmentation requires terabytes of memory. We demonstrate that this bottleneck is not fundamental. Formalizing the information flow of forward selection through a filtration, we show that compatible selectors interact with unselected dummies solely through projections onto an adaptively evolving low-dimensional subspace. For rotationally invariant dummy distributions, we derive an adaptive stick-breaking construction sampling these projections from their exact conditional distribution given the selection history, thereby eliminating dummy matrix materialization. We prove a pathwise universality theorem: under mild delocalization conditions, selection paths driven by generic standardized i.i.d. dummies converge to the same Gaussian limit. We instantiate the theory through Virtual Dummy LARS (VD-LARS), reducing memory and runtime by several orders of magnitude while preserving the exact selection law and FDR guarantees of the T-Rex selector. Experiments on realistic genome-wide association study data confirm that VD-T-Rex controls FDR and achieves power at scales where all competing methods either fail or time out.