Linear Dependency between ε and the Input Noise in ε-Support Vector Regression

Abstract

In using the ε-support vector regression (ε-SVR) algorithm, one has to decide on a suitable value of the insensitivity parameter ε. Smola et al. [6] determined its “optimal” choice based on maximizing the statistical efficiency of a location parameter estimator. While they successfully predicted a linear scaling between the optimal ε and the noise in the data, the value of the theoretically optimal ε does not have a close match with its experimentally observed counterpart. In this paper, we attempt to better explain the experimental results there, by analyzing a toy problem with a closer setting to the ε-SVR. Our resultant predicted choice of ε is much closer to the experimentally observed value, while still demonstrating a linear trend with the data noise.