Sparse quadratic classification rules via linear dimension reduction

TL;DR

This paper introduces a scalable high-dimensional classification method that combines variable selection and linear dimension reduction, enabling effective quadratic discriminant analysis without estimating precision matrices.

Contribution

It proposes a novel framework for quadratic classification that avoids precision matrix estimation and scales linearly with data dimensionality, supported by theoretical guarantees.

Findings

Method performs well on high-dimensional gene expression data.

Theoretical guarantees ensure variable selection consistency.

Application highlights the importance of ESR1 gene in breast cancer classification.

Abstract

We consider the problem of high-dimensional classification between the 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 original data, with the subsequent application of quadratic discriminant analysis on the reduced space. In contrast to quadratic discriminant analysis, the proposed framework doesn't require estimation of precision matrices and 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 comparison with competing approaches. We apply the method to gene expression data of breast cancer patients, and confirm the crucial importance of ESR1 gene in differentiating estrogen receptor status.