Generalized ε-Loss Function-Based Regression

In this paper, we propose a new loss function termed as "generalized epsilon-loss function" to study the regression problem. Unlike the standard epsilon-insensitive loss function, the generalized epsilon-loss function penalizes even those data points which lie inside of the epsilon-tube so as to minimize the scatter within the tube. Also, the rate of penalization of data points lying outside of the epsilon-tube is much higher in comparison to the data points which lie inside of the epsilon-tube. Based on the proposed generalized epsilon-loss function, a new support vector regression model is formulated which is termed as "Penalizing epsilon-generalized SVR (Pen-epsilon-SVR)." Further, extensive numerical experiments are carried out to check the validity and efficacy of the proposed Pen-epsilon-SVR.