Pivotal Estimation of Linear Discriminant Analysis in High Dimensions

TL;DR

This paper introduces PANDA, a high-dimensional linear discriminant analysis method that is tuning-insensitive, achieves optimal convergence rates, and outperforms existing methods in accuracy and ease of use.

Contribution

PANDA is a novel, tuning-insensitive LDA method that attains optimal convergence rates in high-dimensional settings, simplifying parameter tuning and improving performance.

Findings

PANDA achieves optimal convergence rates in estimation and classification.

PANDA outperforms existing methods in accuracy on simulated and real data.

PANDA requires less effort in parameter tuning compared to existing approaches.

Abstract

We consider the linear discriminant analysis problem in the high-dimensional settings. In this work, we propose PANDA(PivotAl liNear Discriminant Analysis), a tuning-insensitive method in the sense that it requires very little effort to tune the parameters. Moreover, we prove that PANDA achieves the optimal convergence rate in terms of both the estimation error and misclassification rate. Our theoretical results are backed up by thorough numerical studies using both simulated and real datasets. In comparison with the existing methods, we observe that our proposed PANDA yields equal or better performance, and requires substantially less effort in parameter tuning.