Bayesian Knockoff Filter

TL;DR

The paper introduces the Bayesian knockoff filter (BKF), a novel method that combines Bayesian inference with the knockoff procedure to improve feature selection accuracy and false discovery rate control in high-dimensional data analysis.

Contribution

It develops a Bayesian framework for knockoff filtering that updates knockoff variables via MCMC, enhancing feature selection performance over existing methods.

Findings

Higher power in detecting true features.

Lower false discovery rate compared to existing methods.

Effective on both synthetic and real datasets.

Abstract

In many scientific fields, researchers are interested in discovering features with substantial effect on the response from a large number of features while controlling the proportion of false discoveries. By incorporating the knockoff procedure in the Bayesian framework, we develop the Bayesian knockoff filter (BKF) for selecting features that have important effect on the response. In contrast to the fixed knockoff variables in a frequentist procedure, we allow the knockoff variables to be continuously updated using the Markov chain Monte Carlo. Based on the posterior samples and the elaborated greedy selection procedure, our method can distinguish the truly important features from unimportant ones and the Bayesian false discovery rate can be controlled at a desirable level. Numerical experiments on both synthetic and real data demonstrate the advantages of our BKF over existing knockoff methods and Bayesian variable selection approaches, i.e., the BKF possesses higher power and yields a lower false discovery rate.