Differentially Private Variable Selection via the Knockoff Filter

TL;DR

This paper introduces a differentially private adaptation of the knockoff filter for variable selection, ensuring controlled false discovery rate while maintaining reasonable statistical power through Gaussian and Laplace mechanisms.

Contribution

It develops a novel private version of the knockoff filter that integrates privacy mechanisms to enable FDR-controlled variable selection.

Findings

Achieves controlled FDR with differential privacy.

Maintains reasonable statistical power in simulations.

Integrates Gaussian and Laplace mechanisms effectively.

Abstract

The knockoff filter, recently developed by Barber and Candes, is an effective procedure to perform variable selection with a controlled false discovery rate (FDR). We propose a private version of the knockoff filter by incorporating Gaussian and Laplace mechanisms, and show that variable selection with controlled FDR can be achieved. Simulations demonstrate that our setting has reasonable statistical power.