A Bandit Approach to Multiple Testing with False Discovery Control
This provides an efficient method for biological sciences, clinical drug testing, and online A/B/n testing where sequential sampling with false discovery control is needed.
The paper tackles the problem of maximizing statistical power while controlling false discoveries in multiple testing scenarios where distributions can be sequentially sampled. The proposed bandit-based algorithm achieves sample complexity matching information-theoretic lower bounds and shows substantial performance improvements over uniform sampling and adaptive elimination methods in simulations.
We propose an adaptive sampling approach for multiple testing which aims to maximize statistical power while ensuring anytime false discovery control. We consider $n$ distributions whose means are partitioned by whether they are below or equal to a baseline (nulls), versus above the baseline (actual positives). In addition, each distribution can be sequentially and repeatedly sampled. Inspired by the multi-armed bandit literature, we provide an algorithm that takes as few samples as possible to exceed a target true positive proportion (i.e. proportion of actual positives discovered) while giving anytime control of the false discovery proportion (nulls predicted as actual positives). Our sample complexity results match known information theoretic lower bounds and through simulations we show a substantial performance improvement over uniform sampling and an adaptive elimination style algorithm. Given the simplicity of the approach, and its sample efficiency, the method has promise for wide adoption in the biological sciences, clinical testing for drug discovery, and online A/B/n testing problems.