Stochastic Hard Thresholding Algorithms for AUC Maximization

TL;DR

This paper introduces a novel stochastic hard thresholding algorithm, SHT-AUC, for AUC maximization in imbalanced classification, achieving linear convergence and efficient computation.

Contribution

It is the first to develop stochastic hard thresholding algorithms for AUC maximization with low per-iteration cost and proven convergence properties.

Findings

Algorithm achieves linear convergence rate.

Performance degrades with increased data imbalance.

Extensive experiments confirm efficiency and effectiveness.

Abstract

In this paper, we aim to develop stochastic hard thresholding algorithms for the important problem of AUC maximization in imbalanced classification. The main challenge is the pairwise loss involved in AUC maximization. We overcome this obstacle by reformulating the U-statistics objective function as an empirical risk minimization (ERM), from which a stochastic hard thresholding algorithm (\texttt{SHT-AUC}) is developed. To our best knowledge, this is the first attempt to provide stochastic hard thresholding algorithms for AUC maximization with a per-iteration cost $\O(b d)$ where $d$ and $b$ are the dimension of the data and the minibatch size, respectively. We show that the proposed algorithm enjoys the linear convergence rate up to a tolerance error. In particular, we show, if the data is generated from the Gaussian distribution, then its convergence becomes slower as the data gets more imbalanced. We conduct extensive experiments to show the efficiency and effectiveness of the proposed algorithms.