Controlled feature selection aims to discover the features a response depends
on while limiting the false discovery rate (FDR) to a predefined level.
Recently, multiple deep-learning-based methods have been proposed to perform
controlled feature selection through the Model-X knockoff framework. We
demonstrate, however, that these methods often fail to control the FDR for two
reasons. First, these methods often learn inaccurate models of features.
Second, the "swap" property, which is required for knockoffs to be valid, is
often not well enforced. We propose a new procedure called FlowSelect that
remedies both of these problems. To more accurately model the features,
FlowSelect uses normalizing flows, the state-of-the-art method for density
estimation. To circumvent the need to enforce the swap property, FlowSelect
uses a novel MCMC-based procedure to calculate p-values for each feature
directly. Asymptotically, FlowSelect computes valid p-values. Empirically,
FlowSelect consistently controls the FDR on both synthetic and semi-synthetic
benchmarks, whereas competing knockoff-based approaches do not. FlowSelect also
demonstrates greater power on these benchmarks. Additionally, FlowSelect
correctly infers the genetic variants associated with specific soybean traits
from GWAS data.Comment: 20 pages, 9 figures, 3 table