Metropolized Knockoff Sampling

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.

References in corpus (6)

• Identification of direct residue contacts in protein-protein interaction by message passing
• Improved contact prediction in proteins: Using pseudolikelihoods to infer Potts models
• Gene Hunting with Knockoffs for Hidden Markov Models
• Deep Knockoffs
• Knockoffs for the mass: new feature importance statistics with false discovery guarantees
• Auto-Encoding Knockoff Generator for FDR Controlled Variable Selection

Cited by in corpus (4)

• Relating the Partial Dependence Plot and Permutation Feature Importance to the Data Generating Process
• Causal Inference in Genetic Trio Studies
• Conditional Feature Importance for Mixed Data
• Can linear algebra create perfect knockoffs?