Improving the Stability of the Knockoff Procedure: Multiple Simultaneous Knockoffs and Entropy Maximization

The Model-X knockoff procedure has recently emerged as a powerful approach for feature selection with statistical guarantees. The advantage of knockoffs is that if we have a good model of the features X, then we can identify salient features without knowing anything about how the outcome Y depends on X. An important drawback of knockoffs is its instability: running the procedure twice can result in very different selected features, potentially leading to different conclusions. Addressing this instability is critical for obtaining reproducible and robust results. Here we present a generalization of the knockoff procedure that we call simultaneous multi-knockoffs. We show that multi-knockoffs guarantee false discovery rate (FDR) control, and are substantially more stable and powerful compared to the standard (single) knockoffs. Moreover we propose a new algorithm based on entropy maximization for generating Gaussian multi-knockoffs. We validate the improved stability and power of multi-knockoffs in systematic experiments. We also illustrate how multi-knockoffs can improve the accuracy of detecting genetic mutations that are causally linked to phenotypes.