Contra: Contrarian statistics for controlled variable selection.

The holdout randomization test (HRT) discovers a set of covariates most predictive of a response. Given the covariate distribution, HRTs can explicitly control the false discovery rate (FDR). However, if this distribution is unknown and must be estimated from data, HRTs can inflate the FDR. To alleviate the inflation of FDR, we propose the contrarian randomization test (CONTRA), which is designed explicitly for scenarios where the covariate distribution must be estimated from data and may even be misspecified. Our key insight is to use an equal mixture of two "contrarian" probabilistic models in determining the importance of a covariate. One model is fit with the real data, while the other is fit using the same data, but with the covariate being tested replaced with samples from an estimate of the covariate distribution. CONTRA is flexible enough to achieve a power of 1 asymptotically, can reduce the FDR compared to state-of-the-art CVS methods when the covariate distribution is misspecified, and is computationally efficient in high dimensions and large sample sizes. We further demonstrate the effectiveness of CONTRA on numerous synthetic benchmarks, and highlight its capabilities on a genetic dataset.