Large dimensional analysis of general margin based classification methods

TL;DR

This paper analyzes the asymptotic performance of various large-margin classifiers in high-dimensional settings, providing insights into classifier selection and parameter tuning for large p and n.

Contribution

It offers a unified asymptotic analysis of multiple margin-based classifiers under high-dimensional regimes, guiding optimal classifier choice and parameter tuning.

Findings

Asymptotic performance characterized by nonlinear equations

Close match between theoretical results and simulations

Guidelines for classifier selection and tuning in high dimensions

Abstract

Margin-based classifiers have been popular in both machine learning and statistics for classification problems. Since a large number of classifiers are available, one natural question is which type of classifiers should be used given a particular classification task. We answer this question by investigating the asymptotic performance of a family of large-margin classifiers under the two component mixture models in situations where the data dimension $p$ and the sample $n$ are both large. This family covers a broad range of classifiers including support vector machine, distance weighted discrimination, penalized logistic regression, and large-margin unified machine as special cases. The asymptotic results are described by a set of nonlinear equations and we observe a close match of them with Monte Carlo simulation on finite data samples. Our analytical studies shed new light on how to select the best classifier among various classification methods as well as on how to choose the optimal tuning parameters for a given method.