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Bayesian inference of noise levels in regression

  • Christopher M. Bishop
  • Cazhaow S. Qazaz
Oral Presentations: Theory Theory II: Learning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1112)

Abstract

In most treatments of the regression problem it is assumed that the distribution of target data can be described by a deterministic function of the inputs, together with additive Gaussian noise having constant variance. The use of maximum likelihood to train such models then corresponds to the minimization of a sum-of-squares error function. In many applications a more realistic model would allow the noise variance itself to depend on the input variables. However, the use of maximum likelihood for training such models would give highly biased results. In this paper we show how a Bayesian treatment can allow for an input-dependent variance while overcoming the bias of maximum likelihood.

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References

  1. Bishop, C. M. (1995). Neural Networks for Pattern Recognition. Oxford University Press.Google Scholar
  2. MacKay, D. J. C. (1991). Bayesian Methods for Adaptive Models. Ph.D. thesis, California Institute of Technology.Google Scholar
  3. MacKay, D. J. C. (1995). Probabilistic networks: new models and new methods. In F. Fogelman-Soulié and P. Gallinari (Eds.), Proceedings ICANN'95 International Conference on Artificial Neural Networks, pp. 331–337. Paris: EC2 & Cie.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Christopher M. Bishop
    • 1
  • Cazhaow S. Qazaz
    • 1
  1. 1.Neural Computing Research GroupAston UniversityBirminghamUK

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