AUC (Area under the ROC curve) is an important performance measure for applications where the data is highly imbalanced. Learning to maximize AUC performance is thus an important research problem. Using a max-margin based surrogate loss function, AUC optimization problem can be approximated as a pairwise rankSVM learning problem. Batch learning methods for solving the kernelized version of this problem suffer from scalability and may not result in sparse classifiers. Recent years have witnessed an increased interest in the development of online or single-pass online learning algorithms that design a classifier by maximizing the AUC performance. The AUC performance of nonlinear classifiers, designed using online methods, is not comparable with that of nonlinear classifiers designed using batch learning algorithms on many real-world datasets. Motivated by these observations, we design a scalable algorithm for maximizing AUC performance by greedily adding the required number of basis functions into the classifier model. The resulting sparse classifiers perform faster inference. Our experimental results show that the level of sparsity achievable can be order of magnitude smaller than the Kernel RankSVM model without affecting the AUC performance much.
 This paper presents a Support Vector Method for optimizing multivariate nonlinear performance measures like the F 1 -score. Taking a multivariate prediction approach, we give an algorithm with which such multivariate SVMs can be trained in polynomial time for large classes of potentially non-linear performance measures, in particular ROCArea and all measures that can be computed from the contingency table. The conventional classification SVM arises as a special case of our method. Learning to rank is an important task for recommendation systems, online advertisement and web search. Among those learning to rank methods, rankSVM is a widely used model. Both linear and nonlinear (kernel) rankSVM have been extensively studied, but the lengthy training time of kernel rankSVM remains a challenging issue. In this paper, after discussing difficulties of training kernel rankSVM, we propose an efficient method to handle these problems. The idea is to reduce the number of variables from quadratic to linear with respect to the number of training instances, and efficiently evaluate the pairwise losses. Our setting is applicable to a variety of loss functions. Further, general optimization methods can be easily applied to solve the reformulated problem. Implementation issues are also carefully considered. Experiments show that our method is faster than state-of-the-art methods for training kernel rankSVM.