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Mean field variational Bayesian inference for support vector machine classification

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  • Luts, Jan
  • Ormerod, John T.

Abstract

A mean field variational Bayes approach to support vector machines (SVMs) using the latent variable representation on Polson and Scott (2012) is presented. This representation allows circumvention of many of the shortcomings associated with classical SVMs including automatic penalty parameter selection, the ability to handle dependent samples, missing data and variable selection. We demonstrate on simulated and real datasets that our approach is easily extendable to non-standard situations and outperforms the classical SVM approach whilst remaining computationally efficient.

Suggested Citation

  • Luts, Jan & Ormerod, John T., 2014. "Mean field variational Bayesian inference for support vector machine classification," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 163-176.
    • Handle: RePEc:eee:csdana:v:73:y:2014:i:c:p:163-176
    DOI: 10.1016/j.csda.2013.10.030
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    References listed on IDEAS

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
    2. Luts, Jan & Molenberghs, Geert & Verbeke, Geert & Van Huffel, Sabine & Suykens, Johan A.K., 2012. "A mixed effects least squares support vector machine model for classification of longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 611-628.
    3. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
    4. Faes, C. & Ormerod, J. T. & Wand, M. P., 2011. "Variational Bayesian Inference for Parametric and Nonparametric Regression With Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 959-971.
    5. Bani K. Mallick & Debashis Ghosh & Malay Ghosh, 2005. "Bayesian classification of tumours by using gene expression data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 219-234, April.
    6. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
    7. Kim, Ji-Hyun, 2009. "Estimating classification error rate: Repeated cross-validation, repeated hold-out and bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3735-3745, September.
    8. M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.
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    Cited by:

    1. Minjeong Jeon & Frank Rijmen & Sophia Rabe-Hesketh, 2017. "A Variational Maximization–Maximization Algorithm for Generalized Linear Mixed Models with Crossed Random Effects," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 693-716, September.
    2. Asim Ansari & Yang Li & Jonathan Z. Zhang, 2018. "Probabilistic Topic Model for Hybrid Recommender Systems: A Stochastic Variational Bayesian Approach," Marketing Science, INFORMS, vol. 37(6), pages 987-1008, November.

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