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Activity Number: 355 - Modern Model Selection
Type: Contributed
Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #312529
Title: Sparse Group LASSO False Discovery Rate Path
Author(s): Kan Chen* and Zhiqi Bu
Companies: and University of Pennsylvania
Keywords: sparse group LASSO; type I/II errors trade-off; phase transition; approximate message passing; proximal algorithm

In this paper, we examine the effects of the group information and the proportion of $\ell_1$ penalty $(\gamma)$ on various performance measures, for both the noisy and noiseless cases, under any sampling rate ($n/p$).We demonstrate that there is a trade-off between the type I and II errors along the SGL path. More specifically, we derive the sharp asymptotic trade-off between true positive proportion (TPP) and false discovery proportion (FDP), consisting of possibly multiple line segments. Similar to LASSO, SGL also suffers from the Donoho-Tanner phase transition (a TPP upper bound) but may additionally have a TPP lower bound. With sufficiently correct group information and smaller $\gamma$, we show that SGL can have significantly better performance measure than LASSO, in terms of TPP, FDP and mean squared error. Furthermore, we investigate the effect of $\gamma$ when the group information is imperfect. Our theoretical analysis leverages the approximate message passing (AMP) theory and properties of the SGL proximal operator. Finally, simulations and real-data experiments are presented to support our results.

Authors who are presenting talks have a * after their name.

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