Sparse quadratic classification rules via linear dimension reduction

Irina Gaynanova and Tianying Wang

Journal of Multivariate Analysis, 2019, vol. 169, issue C, 278-299

Abstract: We consider the problem of high-dimensional classification between two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and linear dimension reduction on the original data, with the subsequent application of quadratic discriminant analysis on the reduced space. In contrast to quadratic discriminant analysis, the proposed framework does not require the estimation of precision matrices; it scales linearly with the number of measurements, making it especially attractive for the use on high-dimensional datasets. We support the methodology with theoretical guarantees on variable selection consistency, and empirical comparisons with competing approaches. We apply the method to gene expression data of breast cancer patients, and confirm the crucial importance of the ESR1 gene in differentiating estrogen receptor status.

Keywords: Convex optimization; Discriminant analysis; High-dimensional statistics; Variable selection (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.jmva.2018.09.011

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