A Univariate Bound of Area Under ROC

TL;DR

This paper introduces a new surrogate loss for AUC optimization that avoids pairwise comparisons, enabling faster and more efficient online and batch learning algorithms for binary classification.

Contribution

It proposes a novel surrogate loss based on AUC risk reformulation that reduces complexity and improves efficiency in AUC optimization.

Findings

The new surrogate loss achieves linear time and storage complexity.

Experimental results show improved efficiency and effectiveness in AUC optimization.

Both online and batch algorithms based on the surrogate perform well in practice.

Abstract

Area under ROC (AUC) is an important metric for binary classification and bipartite ranking problems. However, it is difficult to directly optimizing AUC as a learning objective, so most existing algorithms are based on optimizing a surrogate loss to AUC. One significant drawback of these surrogate losses is that they require pairwise comparisons among training data, which leads to slow running time and increasing local storage for online learning. In this work, we describe a new surrogate loss based on a reformulation of the AUC risk, which does not require pairwise comparison but rankings of the predictions. We further show that the ranking operation can be avoided, and the learning objective obtained based on this surrogate enjoys linear complexity in time and storage. We perform experiments to demonstrate the effectiveness of the online and batch algorithms for AUC optimization based on the proposed surrogate loss.