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In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and the non-smooth part is equipped with a simple proximal mapping. We propose a proximal stochastic second-order method, which is efficient and scalable. It incorporates the Hessian in the smooth part of the function and exploits multistage scheme to reduce the variance of the stochastic gradient. We prove that our method can achieve linear rate of convergence.
In this paper we consider the problem of maximizing the Area under the ROC curve (AUC) which is a widely used performance metric in imbalanced classification and anomaly detection. Due to the pairwise nonlinearity of the objective function, classical
We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic variance-reduced g
In this paper, we consider stochastic second-order methods for minimizing a finite summation of nonconvex functions. One important key is to find an ingenious but cheap scheme to incorporate local curvature information. Since the true Hessian matrix
Recurrent Neural Networks (RNNs) are powerful models that achieve exceptional performance on several pattern recognition problems. However, the training of RNNs is a computationally difficult task owing to the well-known vanishing/exploding gradient
In the application of data clustering to human-centric decision-making systems, such as loan applications and advertisement recommendations, the clustering outcome might discriminate against people across different demographic groups, leading to unfa