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2015 Optimal variable selection in multi-group sparse discriminant analysis
Irina Gaynanova, Mladen Kolar
Electron. J. Statist. 9(2): 2007-2034 (2015). DOI: 10.1214/15-EJS1064

Abstract

This article considers the problem of multi-group classification in the setting where the number of variables $p$ is larger than the number of observations $n$. Several methods have been proposed in the literature that address this problem, however their variable selection performance is either unknown or suboptimal to the results known in the two-group case. In this work we provide sharp conditions for the consistent recovery of relevant variables in the multi-group case using the discriminant analysis proposal of Gaynanova et al. [7]. We achieve the rates of convergence that attain the optimal scaling of the sample size $n$, number of variables $p$ and the sparsity level $s$. These rates are significantly faster than the best known results in the multi-group case. Moreover, they coincide with the minimax optimal rates for the two-group case. We validate our theoretical results with numerical analysis.

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Irina Gaynanova. Mladen Kolar. "Optimal variable selection in multi-group sparse discriminant analysis." Electron. J. Statist. 9 (2) 2007 - 2034, 2015. https://doi.org/10.1214/15-EJS1064

Information

Received: 1 March 2015; Published: 2015
First available in Project Euclid: 31 August 2015

zbMATH: 1323.62060
MathSciNet: MR3393602
Digital Object Identifier: 10.1214/15-EJS1064

Subjects:
Primary: 62H30

Keywords: ‎classification‎ , Fisher’s discriminant analysis , group penalization , High-dimensional statistics

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.9 • No. 2 • 2015
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