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On the consistency theory of high dimensional variable screening
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Wang, Xiangyu, Leng, Chenlei and Dunson, David B. (2015) On the consistency theory of high dimensional variable screening. In: 28th International Conference on Neural Information Processing Systems, Montreal, Canada, 7-12 Dec 2015. Published in: NIPS'15 Proceedings of the 28th International Conference on Neural Information Processing Systems, 2 pp. 2431-2439.
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Official URL: https://dl.acm.org/citation.cfm?id=2969511
Abstract
Variable screening is a fast dimension reduction technique for assisting high dimensional feature selection. As a preselection method, it selects a moderate size subset of candidate variables for further refining via feature selection to produce the final model. The performance of variable screening depends on both computational efficiency and the ability to dramatically reduce the number of variables without discarding the important ones. When the data dimension p is substantially larger than the sample size n, variable screening becomes crucial as 1) Faster feature selection algorithms are needed; 2) Conditions guaranteeing selection consistency might fail to hold. This article studies a class of linear screening methods and establishes consistency theory for this special class. In particular, we prove the restricted diagonally dominant (RDD) condition is a necessary and sufficient condition for strong screening consistency. As concrete examples, we show two screening methods SIS and HOLP are both strong screening consistent (subject to additional constraints) with large probability if n>O((ρs+σ/τ)2logp) under random designs. In addition, we relate the RDD condition to the irrepresentable condition, and highlight limitations of SIS.
Item Type: | Conference Item (Paper) | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Library of Congress Subject Headings (LCSH): | Multivariate analysis | ||||||
Journal or Publication Title: | NIPS'15 Proceedings of the 28th International Conference on Neural Information Processing Systems | ||||||
Publisher: | MIT Press | ||||||
Official Date: | 9 June 2015 | ||||||
Dates: |
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Volume: | 2 | ||||||
Number of Pages: | 33 | ||||||
Page Range: | pp. 2431-2439 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Date of first compliant deposit: | 29 May 2016 | ||||||
Date of first compliant Open Access: | 29 May 2016 | ||||||
Conference Paper Type: | Paper | ||||||
Title of Event: | 28th International Conference on Neural Information Processing Systems | ||||||
Type of Event: | Conference | ||||||
Location of Event: | Montreal, Canada | ||||||
Date(s) of Event: | 7-12 Dec 2015 | ||||||
Open Access Version: |
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