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Generalization Performance of Exchange Monte Carlo Method for Normal Mixture Models

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4224))

Abstract

A normal mixture model, which belongs to singular learning machines, is widely used in statistical pattern recognition. In singular learning machines, the Bayesian learning provides the better generalization performance than the maximum likelihood estimation. However, it needs huge computational cost to realize the Bayesian posterior distribution by the conventional Monte Carlo method. In this paper, we propose that the exchange Monte Carlo method is appropriate for the Bayesian learning in singular learning machines, and experimentally show that it provides better generalization performance in the Bayesian learning of a normal mixture model than the conventional Monte Carlo method.

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References

  • Watanabe, S.: Algebraic analysis for nonidentifiable learning machines. Neural Computation 13(4), 899–933 (2001)

    Article  MATH  Google Scholar 

  • Yamazaki, K., Watanabe, S.: Singularities in mixture models and upper bounds of stochastic complexity. Neural Networks 16(7), 1029–1038 (2003)

    Article  Google Scholar 

  • Nakano, N., Takahashi, K., Watanabe, S.: On the Evaluation Criterion of the MCMC Method in Singular Learning Machines. Trans. of IEICE. J88-D-2(10), 2011–2020 (2005)

    Google Scholar 

  • Iba, Y.: Extended Ensemble Monte Carlo. International Journal of Modern Physics C12, 623–656 (2001)

    Article  Google Scholar 

  • Hukushima, K., Nemoto, K.: Exchange Monte Carlo Method and Application to Spin Glass Simulation. Journal of the Physical Society of Japan 65(6), 1604–1608 (1996)

    Article  MathSciNet  Google Scholar 

  • Sengupta, P., Sandvik, A.W., Campbell, D.K.: Bond-order-wave phase and quantum phase transitions in the one dimensional extended Hubbard model. Physical Review B 65, 155113 (2002)

    Article  Google Scholar 

  • Pinn, K., Wieczerkowski, C.: Number of magic squares from parallel tempering Monte Carlo. Int. J. Mod. Phys. C9, 541 (1998)

    Google Scholar 

  • Hukushima, K.: Extended ensemble Monte Carlo approach to hardly relaxing problems. Computer Physics Communications 147, 77–82 (2002)

    Article  MATH  Google Scholar 

  • Nagata, K., Watanabe, S.: Exchange Monte Carlo Method for Bayesian Learning in Singular Learning Machines. In: Proc of International Joint Conference on Neural Networks (IJCNN2006) (to appear)

    Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Nagata, K., Watanabe, S. (2006). Generalization Performance of Exchange Monte Carlo Method for Normal Mixture Models. In: Corchado, E., Yin, H., Botti, V., Fyfe, C. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2006. IDEAL 2006. Lecture Notes in Computer Science, vol 4224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11875581_15

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  • DOI: https://doi.org/10.1007/11875581_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45485-4

  • Online ISBN: 978-3-540-45487-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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