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2017 Within group variable selection through the Exclusive Lasso
Frederick Campbell, Genevera I. Allen
Electron. J. Statist. 11(2): 4220-4257 (2017). DOI: 10.1214/17-EJS1317

Abstract

Many data sets consist of variables with an inherent group structure. The problem of group selection has been well studied, but in this paper, we seek to do the opposite: our goal is to select at least one variable from each group in the context of predictive regression modeling. This problem is NP-hard, but we propose the tightest convex relaxation: a composite penalty that is a combination of the $\ell_{1}$ and $\ell_{2}$ norms. Our so-called Exclusive Lasso method performs structured variable selection by ensuring that at least one variable is selected from each group. We study our method’s statistical properties and develop computationally scalable algorithms for fitting the Exclusive Lasso. We study the effectiveness of our method via simulations as well as using NMR spectroscopy data. Here, we use the Exclusive Lasso to select the appropriate chemical shift from a dictionary of possible chemical shifts for each molecule in the biological sample.

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Frederick Campbell. Genevera I. Allen. "Within group variable selection through the Exclusive Lasso." Electron. J. Statist. 11 (2) 4220 - 4257, 2017. https://doi.org/10.1214/17-EJS1317

Information

Received: 1 April 2016; Published: 2017
First available in Project Euclid: 26 October 2017

zbMATH: 06805091
MathSciNet: MR3716499
Digital Object Identifier: 10.1214/17-EJS1317

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Vol.11 • No. 2 • 2017
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