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Construction of Bayesian support vector regression in the feature space spanned by Bezier-Bernstein polynomial functions

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Ill-posed inverse problems of recovering nonlinear dependencies in observational data are considered. An inductive method is developed for construction of a Bayesian model of support vector regression in Bernstein form. A new Bayesian evidence criterion is used to compare the adequacy of models.

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References

  1. B. E. Boser, I. M. Guyon, and V. N. Vapnik “A training algorithm for optimal margin classifiers,” in: D. Haussler (ed.), Proc. Annual Conf. on Comput. Learning Theory, ACM Press, Pittsburgh (PA) (1992), 144–152.

    Google Scholar 

  2. V. Vapnik, S. Golowich, and A. Smola, “Support vector method for function approximation, regression estimation, and signal processing,” Advances in Neural Inform. Process. Systems, 9, 281–287, MIT Press, Cambridge (MA) (1997).

    Google Scholar 

  3. A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Statist. and Comput, No. 14, 199–222 (2004).

  4. M. H. Law and J. T. Kwok, “Applying the Bayesian evidence framework to ν-support vector regression,” in: Proc. European Conf. on Machine Learning (ECML), Freiburg, Germany (2001), pp. 312–323.

  5. D. Mackay, “A practical Bayesian framework for backprop networks,” Neural Comput., 4, 448–472 (1992).

    Article  Google Scholar 

  6. W. Chu, S. Keerthi, and C. J. Ong, “Bayesian support vector regression using a unified loss function,” IEEE Trans. on Neural Networks, 15, No. 1, 29–44 (2004).

    Article  Google Scholar 

  7. S. R. Gunn and M. Brown, “SUPANOVA — a sparse, transparent modelling approach,” in: Proc. IEEE Intern. Workshop on Neural Networks for Signal Proces., Madison, Wisconsin (1999), pp. 21–30.

  8. X. Hong and C. J. Harris, “Generalized neurofuzzy network modeling algorithms using Bzier-Bernstein polynomial functions and additive decomposition,” IEEE Trans. Neural Networks, 11, No. 4, 889–902 (2000).

    Article  Google Scholar 

  9. D. Mackay, “Bayesian methods for adaptive models,” Ph. D. Dissertation, California Institute of Technology, Pasadena (1992).

    Google Scholar 

  10. M. Kuss and C. E. Rasmussen, “Assessing approximate inference for binary Gaussian process classification,” J. of Machine Learning Res., No. 6, 1679–1704 (2005).

    Google Scholar 

  11. O. Yu. Mytnik, “Local smoothing of an ε-insensitive loss function in a Bayesian model of support vectors,” in: Proc. IVth Intern. Sci. Conf. “Intellectual Analysis of Information,” Kiev (2006), pp. 189–198.

  12. O. Yu. Mytnik and P. I. Bidyuk, “De Casteljau inverse mapping in fuzzy neural models,” System Investigations and Information Technologies, No. 2, 24–34 (2004).

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Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 179–188, July–August 2007.

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Mytnik, O.Y. Construction of Bayesian support vector regression in the feature space spanned by Bezier-Bernstein polynomial functions. Cybern Syst Anal 43, 613–620 (2007). https://doi.org/10.1007/s10559-007-0087-x

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  • DOI: https://doi.org/10.1007/s10559-007-0087-x

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