  We propose the holdout randomization test (HRT), an approach to feature
selection using black box predictive models. The HRT is a specialized version
of the conditional randomization test (CRT; Candes et al., 2018) that uses data
splitting for feasible computation. The HRT works with any predictive model and
produces a valid $p$-value for each feature. To make the HRT more practical, we
propose a set of extensions to maximize power and speed up computation. In
simulations, these extensions lead to greater power than a competing
knockoffs-based approach, without sacrificing control of the error rate. We
apply the HRT to two case studies from the scientific literature where
heuristics were originally used to select important features for predictive
models. The results illustrate how such heuristics can be misleading relative
to principled methods like the HRT. Code is available at
https://github.com/tansey/hrt.
