In this paper we study four kernel machines for estimating expected shortfall, which are constructed through combinations of support vector quantile regression (SVQR), restricted SVQR (RSVQR), least squares support vector machine (LS-SVM) and support vector expectile regression (SVER). These kernel machines have obvious advantages such that they achieve nonlinear model but they do not require t...

This paper presents data selection procedures for support vector machines (SVM). The purpose of data selection is to reduce the dataset by eliminating as many non support vectors (non-SVs) as possible. Based on the fact that support vectors (SVs) are those vectors close to the decision boundary, data selection keeps only the closest pair vectors of opposite classes. The selected dataset will re...

The time complexity of support vector machines (SVMs) prohibits training on huge datasets with millions data points. Recently, multilevel approaches to train SVMs have been developed allow for time-efficient datasets. While regular perform the entire in one—time-consuming—optimization step, first build a hierarchy problems decreasing size that resemble original problem and then an SVM model eac...