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arXiv · 1411.6311

Optimal variable selection in multi-group sparse discriminant analysis

Irina Gaynanova·Mladen Kolar
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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., 2014. 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 optimal minimax rates for the two-group case. We validate our theoretical results with numerical analysis.

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Irina Gaynanova, Mladen Kolar. 2014-11-23. Optimal variable selection in multi-group sparse discriminant analysis. https://doi.org/10.1214/15-ejs1064

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