Linear Discriminant Analysis with High-dimensional Mixed Variables

TL;DR

This paper introduces a novel high-dimensional classification method for datasets with mixed categorical and continuous variables, using kernel smoothing and penalized likelihood to improve estimation and classification accuracy.

Contribution

It develops a new approach for classifying high-dimensional mixed data by integrating kernel smoothing and separate parameter estimation, addressing challenges of high dimensionality and mixed variable types.

Findings

The proposed classifier achieves competitive misclassification rates.

Estimation accuracy is validated through simulations and real data.

The method effectively handles high-dimensional mixed variables.

Abstract

Datasets containing both categorical and continuous variables are frequently encountered in many areas, and with the rapid development of modern measurement technologies, the dimensions of these variables can be very high. Despite the recent progress made in modelling high-dimensional data for continuous variables, there is a scarcity of methods that can deal with a mixed set of variables. To fill this gap, this paper develops a novel approach for classifying high-dimensional observations with mixed variables. Our framework builds on a location model, in which the distributions of the continuous variables conditional on categorical ones are assumed Gaussian. We overcome the challenge of having to split data into exponentially many cells, or combinations of the categorical variables, by kernel smoothing, and provide new perspectives for its bandwidth choice to ensure an analogue of Bochner's Lemma, which is different to the usual bias-variance tradeoff. We show that the two sets of parameters in our model can be separately estimated and provide penalized likelihood for their estimation. Results on the estimation accuracy and the misclassification rates are established, and the competitive performance of the proposed classifier is illustrated by extensive simulation and real data studies.