On Affine Invariant $L_p$ Depth Classifiers based on an Adaptive Choice of $p$

TL;DR

This paper introduces an adaptive Lp depth classifier that extends data classification methods to a broader class of distributions and proves its Bayes risk consistency, supported by simulations and benchmark tests.

Contribution

It proposes a novel adaptive Lp depth classifier that does not assume elliptic symmetry and establishes its theoretical Bayes risk consistency.

Findings

The classifier performs well on simulated data.

It outperforms some existing classifiers on benchmark datasets.

The method is robust to distributional assumptions.

Abstract

In this article, we use L$_p$ depth for classification of multivariate data, where the value of $p$ is chosen adaptively using observations from the training sample. While many depth based classifiers are constructed assuming elliptic symmetry of the underlying distributions, our proposed L$_p$ depth classifiers cater to a larger class of distributions. We establish Bayes risk consistency of these proposed classifiers under appropriate regularity conditions. Several simulated and benchmark data sets are analyzed to compare their finite sample performance with some existing parametric and nonparametric classifiers including those based on other notions of data depth.