Applying the Bayesian evidence framework to nu-support vector regression

Martin H. Law and James T. Kwok

Abstract: Following previous successes on applying the Bayesian evidence framework to support vector classifiers and the epsilon-support vector regression algorithm, in this paper we extend the evidence framework also to the nu-support vector regression (nu-SVR) algorithm. We show that nu-SVR training implies a prior on the size of the epsilon-tube that is dependent on the number of training patterns. Besides, this prior has properties that are in line with the error-regulating behavior of nu. Under the evidence framework, standard nu-SVR training can then be regarded as performing level one inference, while levels two and three allow automatic adjustments of the regularization and kernel parameters respectively, without the need of a validation set. Furthermore, this Bayesian extension allows computation of the prediction intervals, taking uncertainties of both the weight parameter and the epsilon-tube width into account. Performance of this method is illustrated on both synthetic and real-world data sets.

Proceedings of the European Conference on Machine Learning (ECML), Freiburg, Germany, September 2001.


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