In the realm of machine learning, the data may contain additional attributes, known as privileged information (PI). The main purpose of PI is to assist in the training of the model and then utilize the acquired knowledge to make predictions for unseen samples. Support vector regression (SVR) is an effective regression model, however, it has a low learning speed due to solving a convex quadratic problem (QP) subject to a pair of constraints. In contrast, twin support vector regression (TSVR) is more efficient than SVR as it solves two QPs each subject to one set of constraints. However, TSVR and its variants are trained only on regular features and do not use privileged features for training. To fill this gap, we introduce a fusion of TSVR with learning using privileged information (LUPI) and propose a novel approach called twin support vector regression with privileged information (TSVR+). The regularization terms in the proposed TSVR+ capture the essence of statistical learning theory and implement the structural risk minimization principle. We use the successive overrelaxation (SOR) technique to solve the optimization problem of the proposed TSVR+, which enhances the training efficiency. As far as our knowledge extends, the integration of the LUPI concept into twin variants of regression models is a novel advancement. The numerical experiments conducted on UCI, stock and time series data collectively demonstrate the superiority of the proposed model.

翻译：在机器学习领域中，数据可能包含被称为特权信息的额外属性。特权信息的主要目的是辅助模型训练，随后利用所学知识对未见样本进行预测。支持向量回归是一种有效的回归模型，但由于需要求解受双重约束的凸二次规划问题，其学习速度较慢。相比之下，孪生支持向量回归通过分别求解两个受单约束的二次规划问题，比支持向量回归具有更高的效率。然而，孪生支持向量回归及其变体仅基于常规特征进行训练，并未利用特权特征。为填补这一空白，我们将孪生支持向量回归与基于特权信息的学习相结合，提出一种名为"融合特权信息的孪生支持向量回归"（TSVR+）的新方法。TSVR+中的正则化项捕捉了统计学习理论的本质，并实现了结构风险最小化原则。我们采用逐次超松弛技术求解TSVR+的优化问题，从而提升了训练效率。据我们所知，将基于特权信息的学习概念融入回归模型的孪生变体是一项创新性进展。在UCI数据集、股票数据和时间序列数据上的数值实验共同证明了所提模型的优越性。