  As datasets grow richer, an important challenge is to leverage the full
features in the data to maximize the number of useful discoveries while
controlling for false positives. We address this problem in the context of
multiple hypotheses testing, where for each hypothesis, we observe a p-value
along with a set of features specific to that hypothesis. For example, in
genetic association studies, each hypothesis tests the correlation between a
variant and the trait. We have a rich set of features for each variant (e.g.
its location, conservation, epigenetics etc.) which could inform how likely the
variant is to have a true association. However popular testing approaches, such
as Benjamini-Hochberg's procedure (BH) and independent hypothesis weighting
(IHW), either ignore these features or assume that the features are categorical
or uni-variate. We propose a new algorithm, NeuralFDR, which automatically
learns a discovery threshold as a function of all the hypothesis features. We
parametrize the discovery threshold as a neural network, which enables flexible
handling of multi-dimensional discrete and continuous features as well as
efficient end-to-end optimization. We prove that NeuralFDR has strong false
discovery rate (FDR) guarantees, and show that it makes substantially more
discoveries in synthetic and real datasets. Moreover, we demonstrate that the
learned discovery threshold is directly interpretable.

Methodology;Applications;Machine Learning