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GGM knockoff filter: False discovery rate control for Gaussian graphical models
Author(s) -
Li Jinzhou,
Maathuis Marloes H.
Publication year - 2021
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12430
Subject(s) - graphical model , hyperparameter , gaussian , false discovery rate , graph , computer science , a priori and a posteriori , algorithm , feature (linguistics) , artificial intelligence , pattern recognition (psychology) , mathematics , theoretical computer science , biochemistry , chemistry , physics , philosophy , epistemology , quantum mechanics , gene , linguistics
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 Candès 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 neighbourhood 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.