Two-dimensional solution path for support vector regression

Authors:
Gang Wang;Dit-Yan Yeung;Frederick H. Lochovsky
Affiliations:
Hong Kong University of Science and Technology, Hong Kong, China;Hong Kong University of Science and Technology, Hong Kong, China;Hong Kong University of Science and Technology, Hong Kong, China
Venue:
ICML '06 Proceedings of the 23rd international conference on Machine learning
Year:
2006

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Abstract

Recently, a very appealing approach was proposed to compute the entire solution path for support vector classification (SVC) with very low extra computational cost. This approach was later extended to a support vector regression (SVR) model called ε-SVR. However, the method requires that the error parameter ε be set a priori, which is only possible if the desired accuracy of the approximation can be specified in advance. In this paper, we show that the solution path for ε-SVR is also piecewise linear with respect to ε. We further propose an efficient algorithm for exploring the two-dimensional solution space defined by the regularization and error parameters. As opposed to the algorithm for SVC, our proposed algorithm for ε-SVR initializes the number of support vectors to zero and then increases it gradually as the algorithm proceeds. As such, a good regression function possessing the sparseness property can be obtained after only a few iterations.