Improving the Stability of the Knockoff Procedure: Multiple Simultaneous Knockoffs and Entropy Maximization
Jaime Roquero Gimenez, James Zou
Abstract
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.
BibTeX
@InProceedings{pmlr-v89-gimenez19b,
title = {Improving the Stability of the Knockoff Procedure: Multiple Simultaneous Knockoffs and Entropy Maximization},
author = {Gimenez, Jaime Roquero and Zou, James},
booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics},
pages = {2184--2192},
year = {2019},
editor = {Chaudhuri, Kamalika and Sugiyama, Masashi},
volume = {89},
series = {Proceedings of Machine Learning Research},
month = {16--18 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v89/gimenez19b/gimenez19b.pdf},
url = {https://proceedings.mlr.press/v89/gimenez19b.html},
abstract = {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.}
}