A working likelihood approach to support vector regression with a data-driven insensitivity parameter

The insensitivity parameter in support vector regression determines the set of support vectors that greatly impacts the prediction. A data-driven approach is proposed to determine an approximate value for this insensitivity parameter by minimizing a generalized loss function originating from the likelihood principle. This data-driven support vector regression also statistically standardizes samples using the scale of noises different from conventional response scaling method. Statistical standardization together with probabilistic regularization based on a working likelihood function produces data-dependent values for the hyperparameters including the insensitivity parameter. The exact asymptotical solutions are provided when the noises are normally distributed. Nonlinear and linear numerical simulations with three types of noises (ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon$$\end{document}-Laplacian distribution, normal distribution, and uniform distribution), and in addition, five real benchmark data sets, are used to test the capacity of the proposed method. Based on all the simulations and the five case studies, the proposed support vector regression using a working likelihood, data-driven insensitivity parameter is superior and has lower computational costs.