Square Penalty Support Vector Regression

Support Vector Regression (SVR) is usually pursued using the 2–insensitive loss function while, alternatively, the initial regression problem can be reduced to a properly defined classification one. In either case, slack variables have to be introduced in practical interesting problems, the usual choice being the consideration of linear penalties for them. In this work we shall discuss the solution of an SVR problem recasting it first as a classification problem and working with square penalties. Besides a general theoretical discussion, we shall also derive some consequences for regression problems of the coefficient structure of the resulting SVMs and illustrate the procedure on some standard problems widely used as benchmarks and also over a wind energy forecasting problem.