A semi-supervised framework for diverse multiple hypothesis testing scenarios

Standard multiple testing procedures are designed to report a list of discoveries, or suspected false null hypotheses, given the hypotheses' p-values or test scores. Recently there has been a growing interest in enhancing such procedures by combining additional information with the primary p-value or score. In line with this idea, we develop RESET (REScoring via Estimating and Training), which uses a unique data-splitting protocol that subsequently allows any semi-supervised learning approach to factor in the available side information while maintaining finite sample error rate control. Our practical implementation, RESET Ensemble, selects from an ensemble of classification algorithms so that it is compatible with a range of multiple testing scenarios without the need for the user to select the appropriate one. We apply RESET to both p-value and competition based multiple testing problems and show that RESET is (1) power-wise competitive, (2) fast compared to most tools and (3) able to uniquely achieve finite sample false discovery rate or false discovery exceedance control, depending on the user's preference.