Limits of False Discovery Rate Control with Lasso

• Activity Number: 600
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Weijie Su* and Malgorzata Bogdan and Emmanuel Candes
• Companies: Stanford University and Wroclaw University of Technology and Stanford University
• Keywords: False discovery rate ; Variable selection ; Sparse regression ; Lasso ; Phase transition ; Minimax

Abstract

This work studies the false discovery rate (FDR) control along the Lasso path under a random design matrix. The first of our theorems provides an exact formula of the asymptotic value of FDR when the number of columns in the design matrix diverges to infinity. The second theorem specifies the limits of FDR control by Lasso as a function of the true model sparsity and the ratio of the number of columns and rows of the design matrix. The shape of this "minimax FDR" curve is related to the well known phase transition curve (Donoho and Tanner, 2004), which specifies the limits on the sparsity over which the true model can not be recovered by Lasso. Asymptotic theoretical results are illustrated with simulations, which show that these results are applicable already for moderate sizes of the design matrix. Our analysis uses tools developed theory for approximate message passing (Donoho, Maleki and Montanari, 2009).