Diagonal Discriminant Analysis with Feature Selection for High Dimensional Data

TL;DR

This paper presents multiDA, a high-dimensional discriminant analysis method that combines feature selection with a hybrid model, improving prediction accuracy and interpretability on complex datasets.

Contribution

Introducing multiDA, a novel hybrid discriminant analysis model with integrated feature selection for high-dimensional data.

Findings

Improved prediction accuracy over existing methods

Enhanced interpretability of selected features

Faster algorithm run time

Abstract

We introduce a new method of performing high dimensional discriminant analysis, which we call multiDA. We achieve this by constructing a hybrid model that seamlessly integrates a multiclass diagonal discriminant analysis model and feature selection components. Our feature selection component naturally simplifies to weights which are simple functions of likelihood ratio statistics allowing natural comparisons with traditional hypothesis testing methods. We provide heuristic arguments suggesting desirable asymptotic properties of our algorithm with regards to feature selection. We compare our method with several other approaches, showing marked improvements in regard to prediction accuracy, interpretability of chosen features, and algorithm run time. We demonstrate such strengths of our model by showing strong classification performance on publicly available high dimensional datasets, as well as through multiple simulation studies. We make an R package available implementing our approach.