期刊
ELECTRONIC JOURNAL OF STATISTICS
卷 11, 期 2, 页码 4220-4257出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/17-EJS1317
关键词
Structured variable selection; composite penalty; NMR spectroscopy; Exclusive Lasso
资金
- NSF [0940902, DMS-1264058, DMS-1554821]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1554821] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1264058] Funding Source: National Science Foundation
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 l(1) and l(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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