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A direct approach for sparse quadratic discriminant analysis
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Jiang, Binyan, Wang, Xiangyu and Leng, Chenlei (2018) A direct approach for sparse quadratic discriminant analysis. Journal of Machine Learning Research, 19 (31). pp. 1-37. ISSN 1533-7928.
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WRAP-a-direct-approach-sparse-quadratic-discriminant-analysis-Leng-2018.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (404Kb) | Preview |
Official URL: http://www.jmlr.org/papers/v19/17-285.html
Abstract
Quadratic discriminant analysis (QDA) is a standard tool for classification due to its simplicity and flexibility. Because the number of its parameters scales quadratically with the number of the variables, QDA is not practical, however, when the dimensionality is relatively large. To address this, we propose a novel procedure named DA-QDA for QDA in analyzing high-dimensional data. Formulated in a simple and coherent framework, DA-QDA aims to directly estimate the key quantities in the Bayes discriminant function including quadratic interactions and a linear index of the variables for classification. Under appropriate sparsity assumptions, we establish consistency results for estimating the interactions and the linear index, and further demonstrate that the misclassification rate of our procedure converges to the optimal Bayes risk, even when the dimensionality is exponentially high with respect to the sample size. An efficient algorithm based on the alternating direction method of multipliers (ADMM) is developed for finding interactions, which is much faster than its competitor in the literature. The promising performance of DA-QDA is illustrated via extensive simulation studies and the analysis of four real datasets.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > Q Science (General) | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
Library of Congress Subject Headings (LCSH): | Machine learning, Statistics, Algorithms | |||||||||
Journal or Publication Title: | Journal of Machine Learning Research | |||||||||
Publisher: | M I T Press | |||||||||
ISSN: | 1533-7928 | |||||||||
Official Date: | 2 September 2018 | |||||||||
Dates: |
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Volume: | 19 | |||||||||
Number: | 31 | |||||||||
Page Range: | pp. 1-37 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||
Date of first compliant deposit: | 17 September 2018 | |||||||||
Date of first compliant Open Access: | 17 September 2018 | |||||||||
RIOXX Funder/Project Grant: |
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