Nodewise Knockoffs: False Discovery Rate Control for Gaussian Graphical Models
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Controlling the false discovery rate (FDR) is important for obtaining reliable and reproducible conclusions in scientific research. This paper considers the problem of controlling the finite sample FDR in learning the structure of a Gaussian graphical model (GGM). Most state-of-the-art structure learning methods do not ensure the FDR control, and those that do are all based on p-values and multiple testing procedures. In this paper, we tackle this problem from a different angle by using the recently proposed knockoff idea of Barber and Candès. Our approach consists of two steps: (a) constructing knockoffs and feature statistics nodewisely; (b) applying a graph-wide rule in choosing the thresholds for each node and then recovering the structure of the graph. The finite sample FDR control property of this approach is shown. In addition, we use a sample-splitting-recycling procedure that first uses half of the sample to select hyperparameters, then learns the structure of the graph using all samples in a certain way such that the FDR control property still holds. Finally, we examine our methodology using simulations and a real data set.
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