On robust twin support vector regression in primal using squared pinball loss

Abstract

Construction of robust regression learning models to fit training data corrupted by noise is an important and challenging research problem in machine learning. It is well-known that loss functions play an important role in reducing the effect of noise present in the input data. With the objective of obtaining a robust regression model, motivated by the link between the pinball loss and quantile regression, a novel squared pinball loss twin support vector machine for regression (SPTSVR) is proposed in this work. Further with the introduction of a regularization term, our proposed model solves a pair of strongly convex minimization problems having unique solutions by simple functional iterative method. Experiments were performed on synthetic datasets with different noise models and on real world datasets and those results were compared with support vector regression (SVR), least squares support vector regression (LS-SVR) and twin support vector regression (TSVR) methods. The comparative results clearly show that our proposed SPTSVR is an effective and a useful addition in the machine learning literature.