A Locally Adaptive Shrinkage Approach to False Selection Rate Control in High-Dimensional Classification

TL;DR

This paper introduces a locally adaptive shrinkage method called LASS for controlling the false selection rate in high-dimensional classification, offering robust theoretical guarantees and practical effectiveness.

Contribution

It develops a new LASS framework for FSR control in high-dimensional LDA that is easy to analyze and performs well across different sparsity regimes.

Findings

LASS effectively controls FSR in simulations and real data.

Theoretical guarantees are established without strong sparsity assumptions.

LASS demonstrates robustness across sparse and dense high-dimensional settings.

Abstract

The uncertainty quantification and error control of classifiers are crucial in many high-consequence decision-making scenarios. We propose a selective classification framework that provides an indecision option for any observations that cannot be classified with confidence. The false selection rate (FSR), defined as the expected fraction of erroneous classifications among all definitive classifications, provides a useful error rate notion that trades off a fraction of indecisions for fewer classification errors. We develop a new class of locally adaptive shrinkage and selection (LASS) rules for FSR control in the context of high-dimensional linear discriminant analysis (LDA). LASS is easy-to-analyze and has robust performance across sparse and dense regimes. Theoretical guarantees on FSR control are established without strong assumptions on sparsity as required by existing theories in high-dimensional LDA. The empirical performances of LASS are investigated using both simulated and real data.