In this paper, a novel and efficient pairing support vector regression learning method using $\epsilon -$insensitive Huber loss function (PHSVR) is proposed where the $\epsilon -$insensitive zone having flexible shape is determined by tightly fitting the training samples. Our approach leads to solving a pair of unconstrained minimization problems in primal and the solutions are obtained by two algorithms: a functional iterative (FPHSVR) and Newton iterative (NPHSVR) algorithms. The finite termination of the Newton method to its global minimum solution is proved. The significant advantages of the proposed method are the robustness, generalization ability and learning speed. Experiments performed on a series of synthetic data sets, polluted by different types of noise including heteroscedastic noise and outliers, and on real-world benchmark data sets confirm the effectiveness and superiority of the proposed method.

本文提出了一种新颖高效的配对支持向量回归学习方法 $\epsilon -$不敏感的Huber损失函数（PHSVR）提出了 $\epsilon -$通过紧密拟合训练样本来确定具有柔性形状的不敏感区域。我们的方法导致解决了原始中的一对无约束最小化问题，并且通过两种算法获得了解决方案：函数迭代（FPHSVR）和牛顿迭代（NPHSVR）算法。证明了牛顿法对其全局最小解的有限终止。该方法的显着优点是鲁棒性，泛化能力和学习速度。在一系列合成数据集上进行的实验受到了包括异方差噪声和异常值在内的不同类型噪声的污染，并在现实世界中的基准数据集上进行了验证，证明了该方法的有效性和优越性。