Pair- ${v}$ -SVR: A Novel and Efficient Pairing nu-Support Vector Regression Algorithm

This paper proposes a novel and efficient pairing nu-support vector regression (pair-v-SVR) algorithm that combines successfully the superior advantages of twin support vector regression (TSVR) and classical ε-SVR algorithms. In spirit of TSVR, the proposed pair-v-SVR solves two quadratic programming problems (QPPs) of smaller size rather than a single larger QPP, and thus has faster learning speed than classical ε-SVR. The significant advantage of our pair-v-SVR over TSVR is the improvement in the prediction speed and generalization ability by introducing the concepts of the insensitive zone and the regularization term that embodies the essence of statistical learning theory. Moreover, pair-v-SVR has additional advantage of using parameter v for controlling the bounds on fractions of SVs and errors. Furthermore, the upper bound and lower bound functions of the regression model estimated by pair-v-SVR capture well the characteristics of data distributions, thus facilitating automatic estimation of the conditional mean and predictive variance simultaneously. This may be useful in many cases, especially when the noise is heteroscedastic and depends strongly on the input values. The experimental results validate the superiority of our pair-v-SVR in both training/prediction speed and generalization ability.