TSVR+: Twin support vector regression with privileged information

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.