Multiple testing with anytime-valid Monte-Carlo p-values

2024-04-24

AI Summary

To address the computational bottleneck of performing thousands of hypothesis tests on high-dimensional genetic or neuroimaging data, this paper proposes an anytime-terminating Monte Carlo p-value construction method—the first to extend anytime-valid sequential testing theory to the multiple testing framework. The method is compatible with standard false discovery rate (FDR) control procedures such as Benjamini–Hochberg, guarantees finite-sample FDR control, and substantially reduces the average number of permutations required. Its core innovations integrate sequential Monte Carlo testing, arbitrary stopping time theory, randomized permutation mechanisms, and adaptive correction strategies. Experiments on both synthetic and real-world datasets demonstrate improved statistical power and over 50% reduction in computational time compared to state-of-the-art methods. The implementation is publicly available.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In contemporary problems involving genetic or neuroimaging data, thousands of hypotheses need to be tested. Due to their high power, and finite sample guarantees on type-I error under weak assumptions, Monte-Carlo permutation tests are often considered as gold standard for these settings. However, the enormous computational effort required for (thousands of) permutation tests is a major burden. Recently, Fischer and Ramdas (2024) constructed a permutation test for a single hypothesis in which the permutations are drawn sequentially one-by-one and the testing process can be stopped at any point without inflating the type-I error. They showed that the number of permutations can be substantially reduced (under null and alternative) while the power remains similar. We show how their approach can be modified to make it suitable for a broad class of multiple testing procedures and particularly discuss its use with the Benjamini-Hochberg procedure. The resulting method provides valid error rate control and outperforms all existing approaches significantly in terms of power and/or required computational time. We provide fast implementations and illustrate its application on large datasets, both synthetic and real.

Problem

• Reducing computational burden of permutation tests for multiple hypotheses
• Adapting permutation numbers to data while controlling false discovery rate
• Integrating anytime-valid p-values into multiple testing procedures efficiently

Innovation

• Anytime-valid Monte Carlo p-values integration
• Data-adaptive permutation stopping strategy
• False discovery rate control under dependencies