STAR: A general interactive framework for FDR control under structural constraints

TL;DR

STAR is a flexible, interactive framework for controlling the false discovery rate in multiple testing problems with complex structural constraints, combining accumulation tests and data-carving for adaptive, finite-sample FDR control.

Contribution

It introduces a novel interactive protocol that allows flexible adaptation to structural constraints while controlling FDR, extending to various applications including regression with knockoff statistics.

Findings

STAR effectively controls FDR in complex structural testing scenarios.

The framework adapts to diverse applications like convex region detection and DAGs.

It extends to regression problems using knockoff statistics.

Abstract

We propose a general framework based on selectively traversed accumulation rules (STAR) for interactive multiple testing with generic structural constraints on the rejection set. It combines accumulation tests from ordered multiple testing with data-carving ideas from post-selection inference, allowing for highly flexible adaptation to generic structural information. Our procedure defines an interactive protocol for gradually pruning a candidate rejection set, beginning with the set of all hypotheses and shrinking with each step. By restricting the information at each step via a technique we call masking, our protocol enables interaction while controlling the false discovery rate (FDR) in finite samples for any data-adaptive update rule that the analyst may choose. We suggest update rules for a variety of applications with complex structural constraints, show that STAR performs well for problems ranging from convex region detection to FDR control on directed acyclic graphs, and show how to extend it to regression problems where knockoff statistics are available in lieu of $p$-values.