A Univariate Bound of Area Under ROC
This addresses efficiency issues in AUC optimization for machine learning practitioners, though it appears incremental as it builds on existing surrogate loss methods.
The paper tackles the challenge of directly optimizing the Area Under ROC (AUC) metric in binary classification by introducing a new surrogate loss that avoids pairwise comparisons, resulting in algorithms with linear time and storage complexity.
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.