Comparison theorems on large-margin learning

TL;DR

This paper introduces comparison theorems for large-margin unified machines (LUM), bridging likelihood and margin approaches, and addresses data piling issues in high-dimensional, low-sample scenarios.

Contribution

It establishes new comparison theorems for LUM loss functions, aiding error analysis and improving understanding of large-margin learning algorithms.

Findings

New comparison theorems for LUM loss functions

Addresses data piling in high-dimensional, low-sample settings

Facilitates error analysis of large-margin classifiers

Abstract

This paper studies binary classification problem associated with a family of loss functions called large-margin unified machines (LUM), which offers a natural bridge between distribution-based likelihood approaches and margin-based approaches. It also can overcome the so-called data piling issue of support vector machine in the high-dimension and low-sample size setting. In this paper we establish some new comparison theorems for all LUM loss functions which play a key role in the further error analysis of large-margin learning algorithms.