Optimal $\gamma$ and $C$ for $\epsilon$-Support Vector Regression with RBF Kernels

TL;DR

This paper investigates how to efficiently select the hyperparameters $C$ and $\gamma$ for $\epsilon$-Support Vector Regression with RBF kernels, linking geometric distances in feature space to prediction accuracy.

Contribution

The study proposes a novel method for determining optimal $C$ and $\gamma$ values based on geometric and statistical considerations in the feature space.

Findings

Identifies the relationship between kernel parameters and prediction accuracy.

Provides a method to select optimal hyperparameters for $\epsilon$-SVR.

Demonstrates improved prediction performance with the proposed parameter selection.

Abstract

The objective of this study is to investigate the efficient determination of $C$ and $\gamma$ for Support Vector Regression with RBF or mahalanobis kernel based on numerical and statistician considerations, which indicates the connection between $C$ and kernels and demonstrates that the deviation of geometric distance of neighbour observation in mapped space effects the predict accuracy of $\epsilon$-SVR. We determinate the arrange of $\gamma$ & $C$ and propose our method to choose their best values.