Within group variable selection through the exclusive Lasso. (English) Zbl 1408.62132

Campbell, Frederick; Allen, Genevera I.

Electron. J. Stat. 11, No. 2, 4220-4257 (2017).

The authors of the paper under review consider regression problems with a predefined group structure to the end of accurately predicting the response using a subset of variables consisting of at least one variable from each group. In order to “directly enforce the desired structure” they present a “methodology for sparse regression with the exclusive Lasso, a convex penalty first introduced by Y. Zhou et al. [“Exclusive Lasso for multi-task feature selection”, Proc. Mach. Learn. Res. (PMLR) 9, 988–995 (2010)] in the context of multi-task learning”. Next, statistical properties of the introduced methodology are studied and two algorithms for fitting the exclusive Lasso are provided. The effectiveness of the methodology is then studied via simulations as well as using Nuclear Magnetic Resonance spectroscopy data.

Reviewer: Joseph Melamed (Los Angeles)

MSC:

62J07	Ridge regression; shrinkage estimators (Lasso)
62P35	Applications of statistics to physics

Keywords:

structured variable selection; composite penalty; NMR spectroscopy; exclusive Lasso