Deep Knockoffs

Abstract

This paper introduces a machine for sampling approximate model-X knockoffs for arbitrary and unspecified data distributions using deep generative models. The main idea is to iteratively refine a knockoff sampling mechanism until a criterion measuring the validity of the produced knockoffs is optimized; this criterion is inspired by the popular maximum mean discrepancy in machine learning and can be thought of as measuring the distance to pairwise exchangeability between original and knockoff features. By building upon the existing model-X framework, we thus obtain a flexible and model-free statistical tool to perform controlled variable selection. Extensive numerical experiments and quantitative tests confirm the generality, effectiveness, and power of our deep knockoff machines. Finally, we apply this new method to a real study of mutations linked to changes in drug resistance in the human immunodeficiency virus.

arXiv comment37 pages, 23 figures, 1 table

References in corpus (19)

• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
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Cited by in corpus (10)

• Metropolized Knockoff Sampling
• Rejoinder: "Gene Hunting with Hidden Markov Model Knockoffs"
• Kernel Two-Sample Tests in High Dimension: Interplay Between Moment Discrepancy and Dimension-and-Sample Orders
• Conditional Feature Importance for Mixed Data
• Controlling the False Discovery Rate in Transformational Sparsity: Split Knockoffs
• Interpretable Classification of Bacterial Raman Spectra with Knockoff Wavelets
• Aggregating Knockoffs for False Discovery Rate Control with an Application to Gut Microbiome Data
• Efficient Multimodal Sampling via Tempered Distribution Flow
• Learning to Increase the Power of Conditional Randomization Tests
• Can linear algebra create perfect knockoffs?