Double Descent in High-dimensional Linear Discriminant Analysis

Abstract

The double-descent phenomenon observed in modern machine learning models has challenged the classical bias-variance trade-off by showing that prediction error can decrease again as model complexity exceeds the interpolation threshold. Although this phenomenon has been extensively studied for deep neural networks and other high-capacity models, its implications for classical statistical methods remain less well understood. In this paper, we investigate double descent in linear discriminant analysis (LDA), a fundamental classification method for binary classification. Using random matrix theory, we derive the asymptotic misclassification risk of LDA in the high-dimensional regime where the dimension (p) and sample size (n) satisfy (p/n \to γ). Specifically, we obtain an explicit asymptotic expression for the LDA risk with a general population covariance matrix when (γ\in (0,1)), and for the Moore-Penrose pseudo-inverse LDA classifier under an isotropic covariance model when (γ\in (1,\infty)). Together, these results provide a complete characterization of the double-descent risk curve of LDA across both the under- and over-parameterized regimes. Simulation studies and experiments on the ARCENE cancer classification dataset demonstrate close agreement with the theoretical predictions.