Metropolized Knockoff Sampling

TL;DR

This paper presents a general and efficient method for generating knockoff variables using a Metropolis-Hastings approach, enabling more effective feature selection with controlled false positives in complex models.

Contribution

It introduces a novel Metropolis-Hastings-based framework for exact knockoff sampling, leveraging conditional independence to improve computational efficiency and applicability.

Findings

Effective knockoff sampling in complex models

Near-optimal computational complexity achieved

Applicable to continuous, heavy-tailed, and graphical models

Abstract

Model-X knockoffs is a wrapper that transforms essentially any feature importance measure into a variable selection algorithm, which discovers true effects while rigorously controlling the expected fraction of false positives. A frequently discussed challenge to apply this method is to construct knockoff variables, which are synthetic variables obeying a crucial exchangeability property with the explanatory variables under study. This paper introduces techniques for knockoff generation in great generality: we provide a sequential characterization of all possible knockoff distributions, which leads to a Metropolis-Hastingsformulation of an exact knockoff sampler. We further show how to use conditional independence structure to speed up computations. Combining these two threads, we introduce an explicit set of sequential algorithms and empirically demonstrate their effectiveness. Our theoretical analysis proves that our algorithms achieve near-optimal computational complexity in certain cases. The techniques we develop are sufficiently rich to enable knockoff sampling in challenging models including cases where the covariates are continuous and heavy-tailed, and follow a graphical model such as the Ising model.