Prediction and estimation consistency of sparse multi-class penalized optimal scoring

TL;DR

This paper establishes probabilistic bounds for prediction and estimation errors in high-dimensional sparse multi-class penalized optimal scoring, extending the understanding of its theoretical properties.

Contribution

It provides the first probabilistic bounds on prediction and estimation consistency for multi-class penalized optimal scoring with diverging classes.

Findings

Bounded out-of-sample prediction error

Bounded estimation error in high dimensions

Applicable to diverging number of classes

Abstract

Sparse linear discriminant analysis via penalized optimal scoring is a successful tool for classification in high-dimensional settings. While the variable selection consistency of sparse optimal scoring has been established, the corresponding prediction and estimation consistency results have been lacking. We bridge this gap by providing probabilistic bounds on out-of-sample prediction error and estimation error of multi-class penalized optimal scoring allowing for diverging number of classes.