Stochastic AUC Optimization Algorithms With Linear Convergence

Michael Natole,Siwei Lyu,Yiming Ying

doi:10.3389/fams.2019.00030

Abstract

Area under the ROC curve (AUC) is a standard metric that is used to measure classification performance for imbalanced class data. Developing stochastic learning algorithms that maximize AUC over accuracy is of practical interest. However, AUC maximization presents a challenge since the learning objective function is defined over a pair of instances of opposite classes. Existing methods circumvent this issue but with high space and time complexity. From our previous work of redefining AUC optimization as a convex-concave saddle point problem, we propose a new stochastic batch learning algorithm for AUC maximization. The key difference from our previous work is that we assume that the underlying distribution of the data is uniform, and we develop a batch learning algorithm that is a stochastic primal-dual algorithm (SPDAM) that achieves a linear convergence rate. We establish the theoretical convergence of SPDAM with high probability and demonstrate its effectiveness on standard benchmark datasets.

Highlights

Quantifying machine learning performance is an important issue to consider when designing learning algorithms
These results show that stochastic primal-dual algorithm (SPDAM) and OAMgra online Uni-Exp B-Support Vector Machines (SVM)-OR
We proposed a stochastic primal-dual algorithm for Area under the ROC curve (AUC) optimization [18, 22] based upon our previous work that AUC maximization is equivalent to a stochastic saddle point problem

Summary

Introduction

Quantifying machine learning performance is an important issue to consider when designing learning algorithms. Optimizing accuracy is not suitable for important learning tasks such as imbalanced classification To overcome these issues, Area Under the ROC Curve (AUC) [2, 3] is a standard metric for quantifying machine learning performance. Area Under the ROC Curve (AUC) [2, 3] is a standard metric for quantifying machine learning performance It is used in many real world applications, such as ranking and anomaly detection. AUC concerns the overall performance of a functional family of classifiers and quantifies their ability of correctly ranking any positive instance with regards to a randomly chosen negative instance This combined with the fact that AUC is not effected by imbalanced class data makes AUC a more robust metric than accuracy [4]. We will discuss maximizing AUC in a batch learning setting

Methods

Results

Conclusion