A new solution path algorithm in support vector regression

In this paper, regularization path algorithms were proposed as a novel approach to the model selection problem by exploring the path of possibly all solutions with respect to some regularization hyperparameter in an efficient way. This approach was later extended to a support vector regression (SVR) model called epsilon-SVR. However, the method requires that the error parameter epsilon be set a priori. This is only possible if the desired accuracy of the approximation can be specified in advance. In this paper, we analyze the solution space for epsilon-SVR and propose a new solution path algorithm, called epsilon-path algorithm, which traces the solution path with respect to the hyperparameter epsilon rather than lambda. Although both two solution path algorithms possess the desirable piecewise linearity property, our epsilon-path algorithm overcomes some limitations of the original lambda-path algorithm and has more advantages. It is thus more appealing for practical use.