A Spatial-Sign based Direct Approach for High Dimensional Sparse Quadratic Discriminant Analysis

ICLR 2026 Conference Submission18975 Authors

Keywords: High dimensional data, Quadratic discriminant analysis, Spatial-sign

TL;DR: Spatial-sign based High Dimensional Sparse Quadratic Discriminant Analysis for Elliptically Symmetric Distribution.

Abstract:

In this paper, we study the problem of high-dimensional sparse quadratic discriminant
analysis (QDA). We propose a novel classification method, termed SSQDA, which is
constructed via constrained convex optimization based on the sample spatial median
and spatial sign covariance matrix under the assumption of an elliptically symmetric
distribution. The proposed classifier is shown to achieve the optimal convergence rate over
a broad class of parameter spaces, up to a logarithmic factor. Extensive simulation studies
and real data applications demonstrate that SSQDA is both robust and efficient, particu-
larly in the presence of heavy-tailed distributions, highlighting its practical advantages in
high-dimensional classification tasks.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Submission Number: 18975