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Optimal variable selection in multi-group sparse discriminant analysis. (English) Zbl 1323.62060

Summary: 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 the first author et al. [“Simultaneous sparse estimation of canonical vectors in the \(p\gg n\) setting”, Preprint, arXiv:1403.6095]. 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.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)

Software:

rda; penalizedLDA
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Full Text: DOI arXiv Euclid

References:

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