Statistics Papers

Document Type

Journal Article

Date of this Version

2011

Publication Source

Journal of the American Statistical Association

Volume

106

Issue

496

Start Page

1566

Last Page

1577

DOI

10.1198/jasa.2011.tm11199

Abstract

This article considers sparse linear discriminant analysis of high-dimensional data. In contrast to the existing methods which are based on separate estimation of the precision matrix Ω and the difference δ of the mean vectors, we introduce a simple and effective classifier by estimating the product Ωδ directly through constrained ℓ1 minimization. The estimator can be implemented efficiently using linear programming and the resulting classifier is called the linear programming discriminant (LPD) rule. The LPD rule is shown to have desirable theoretical and numerical properties. It exploits the approximate sparsity of Ωδ and as a consequence allows cases where it can still perform well even when Ω and/or δ cannot be estimated consistently. Asymptotic properties of the LPD rule are investigated and consistency and rate of convergence results are given. The LPD classifier has superior finite sample performance and significant computational advantages over the existing methods that require separate estimation of Ω and δ. The LPD rule is also applied to analyze real datasets from lung cancer and leukemia studies. The classifier performs favorably in comparison to existing methods.

Copyright/Permission Statement

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 24 Jan 2012, available online: http://wwww.tandfonline.com/10.1198/jasa.2011.tm11199.

Keywords

classification, Constrained l1 minimization, Fisher's rule, Naive Bayes rule, sparsity

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Date Posted: 27 November 2017