The Library
Dynamic linear discriminant analysis in high dimensional space
Tools
Jiang, B., Chen, Z and Leng, Chenlei (2020) Dynamic linear discriminant analysis in high dimensional space. Bernoulli, 26 (2). pp. 1234-1268. doi:10.3150/19-BEJ1154 ISSN 1350-7265.
|
PDF
WRAP-dynamic-linear-discriminant-analysis-high-space-Leng-2020.pdf - Published Version - Requires a PDF viewer. Download (1381Kb) | Preview |
|
PDF
st-191119-wrap--dlda_bernoulli.pdf - Accepted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (1962Kb) |
Official URL: https://doi.org/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.
Item Type: | Journal Article | ||||||
---|---|---|---|---|---|---|---|
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Journal or Publication Title: | Bernoulli | ||||||
Publisher: | International Statistical Institute | ||||||
ISSN: | 1350-7265 | ||||||
Official Date: | 31 January 2020 | ||||||
Dates: |
|
||||||
Volume: | 26 | ||||||
Number: | 2 | ||||||
Page Range: | pp. 1234-1268 | ||||||
DOI: | 10.3150/19-BEJ1154 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 26 November 2019 | ||||||
Date of first compliant Open Access: | 7 February 2020 | ||||||
Related URLs: | |||||||
Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year