GGM knockoff filter: False Discovery Rate Control for Gaussian Graphical Models

TL;DR

This paper introduces a flexible method for learning Gaussian graphical models with finite sample false discovery rate control, extending the knockoff framework to the graphical model setting with local and global steps.

Contribution

It extends the knockoff framework to Gaussian graphical models, providing a novel approach with hyperparameter selection and FDR control in finite samples.

Findings

Method effectively controls FDR in simulations

Flexible approach with various choices of knockoffs and statistics

Outperforms competitors in real data experiments

Abstract

We propose a new method to learn the structure of a Gaussian graphical model with finite sample false discovery rate control. Our method builds on the knockoff framework of Barber and Cand\`{e}s for linear models. We extend their approach to the graphical model setting by using a local (node-based) and a global (graph-based) step: we construct knockoffs and feature statistics for each node locally, and then solve a global optimization problem to determine a threshold for each node. We then estimate the neighborhood of each node, by comparing its feature statistics to its threshold, resulting in our graph estimate. Our proposed method is very flexible, in the sense that there is freedom in the choice of knockoffs, feature statistics, and the way in which the final graph estimate is obtained. For any given data set, it is not clear a priori what choices of these hyperparameters are optimal. We therefore use a sample-splitting-recycling procedure that first uses half of the samples to select the hyperparameters, and then learns the graph using all samples, in such a way that the finite sample FDR control still holds. We compare our method to several competitors in simulations and on a real data set.