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May 2020 Dynamic linear discriminant analysis in high dimensional space
Binyan Jiang, Ziqi Chen, Chenlei Leng
Bernoulli 26(2): 1234-1268 (May 2020). DOI: 10.3150/19-BEJ1154

Abstract

High-dimensional data that evolve dynamically feature predominantly in the modern data era. As a partial response to this, recent years have seen increasing emphasis to address the dimensionality challenge. However, the non-static nature of these datasets is largely ignored. This paper addresses both challenges by proposing a novel yet simple dynamic linear programming discriminant (DLPD) rule for binary classification. Different from the usual static linear discriminant analysis, the new method is able to capture the changing distributions of the underlying populations by modeling their means and covariances as smooth functions of covariates of interest. Under an approximate sparse condition, we show that the conditional misclassification rate of the DLPD rule converges to the Bayes risk in probability uniformly over the range of the variables used for modeling the dynamics, when the dimensionality is allowed to grow exponentially with the sample size. The minimax lower bound of the estimation of the Bayes risk is also established, implying that the misclassification rate of our proposed rule is minimax-rate optimal. The promising performance of the DLPD rule is illustrated via extensive simulation studies and the analysis of a breast cancer dataset.

Citation

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Binyan Jiang. Ziqi Chen. Chenlei Leng. "Dynamic linear discriminant analysis in high dimensional space." Bernoulli 26 (2) 1234 - 1268, May 2020. https://doi.org/10.3150/19-BEJ1154

Information

Received: 1 August 2017; Revised: 1 January 2019; Published: May 2020
First available in Project Euclid: 31 January 2020

zbMATH: 07166562
MathSciNet: MR4058366
Digital Object Identifier: 10.3150/19-BEJ1154

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

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Vol.26 • No. 2 • May 2020
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