The quantile-based classifier with variable-wise parameters

TL;DR

This paper introduces an enhanced quantile-based classifier that optimizes variable-specific parameters and scales, improving classification accuracy in high-dimensional data, with proven consistency and validated through experiments.

Contribution

It extends existing quantile classifiers by allowing variable-wise optimal quantile percentages and scale parameters, with a proven consistency in a nonparametric setting.

Findings

Improved classification performance on high-dimensional data.

Proven consistency of the new method.

Successful validation with artificial and real datasets.

Abstract

Quantile-based classifiers can classify high-dimensional observations by minimising a discrepancy of an observation to a class based on suitable quantiles of the within-class distributions, corresponding to a unique percentage for all variables. The present work extends these classifiers by introducing a way to determine potentially different optimal percentages for different variables. Furthermore, a variable-wise scale parameter is introduced. A simple greedy algorithm to estimate the parameters is proposed. Their consistency in a nonparametric setting is proved. Experiments using artificially generated and real data confirm the potential of the quantile-based classifier with variable-wise parameters.