  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.
