Abstract
Following previous successes on applying the Bayesian evidence framework to support vector classifiers and the ε-support vector regression algorithm, in this paper we extend the evidence framework also to the ν-support vector regression (ν-SVR) algorithm. We show that ν-SVR training implies a prior on the size of the ε-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 ν. Under the evidence framework, standard ν-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 ε-tube width into account. Performance of this method is illustrated on both synthetic and real-world data sets.
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C. Blake, E. Keogh, and C.J. Merz. UCI repository of machine learning databases, 1998. http://www.ics.uci.edu/~mlearn/MLRepository.html University of California, Irvine, Department of Information and Computer Sciences.
J.T. Kwok. Moderating the outputs of support vector machine classifiers. IEEE Transactions on Neural Networks, 10:1018–1031, 1999.
J.T. Kwok. The evidence framework applied to support vector machines. IEEE Transactions on Neural Networks, 11(5):1162–1173, 2000.
D.J.C. MacKay. Bayesian interpolation. Neural Computation, 4(3):415–447, May 1992.
B. Schölkopf and A.J. Smola. New support vector algorithms. NeuroCOLT2 Technical Report NC2-TR-1998-031, GMD FIRST, 1998.
A.J. Smola, N. Murata, B. Scholkopf, and K.-R. Muller. Asymptotically optimal choice of ε-loss for support vector machines. In Proceedings of the International Conference on Artificial Neural Networks, 1998.
A.J. Smola and B. Scholkopf. A tutorial on support vector regression. NeuroCOLT2 Technical Report NC2-TR-1998-030, Royal Holloway College, 1998.
V. Vapnik. Statistical Learning Theory. Wiley, 1998.
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Law, M.H., Kwok, J.T. (2001). Applying the Bayesian Evidence Framework to ν-Support Vector Regression. In: De Raedt, L., Flach, P. (eds) Machine Learning: ECML 2001. ECML 2001. Lecture Notes in Computer Science(), vol 2167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44795-4_27
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DOI: https://doi.org/10.1007/3-540-44795-4_27
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