Regression with input-dependent noise: A Bayesian treatment

Christopher M. Bishop, Cazhaow S. Qazaz

    Research output: Chapter in Book/Report/Conference proceedingChapter

    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 to train 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.
    Original languageEnglish
    Title of host publicationAdvances in Neural Information Processing Systems 9
    EditorsMichael C. Mozer, Michael I. Jordan, Thomas Petsche
    PublisherMIT
    Pages347-353
    Number of pages7
    Volume9
    ISBN (Print)0262100657
    Publication statusPublished - May 1997
    EventAdvances in Neural Information Processing Systems 1994 - Singapore, Singapore
    Duration: 16 Nov 199418 Nov 1994

    Publication series

    NameProceeding of the 1996 conference
    PublisherMassachusetts Institute of Technology Press (MIT Press)

    Other

    OtherAdvances in Neural Information Processing Systems 1994
    CountrySingapore
    CitySingapore
    Period16/11/9418/11/94

    Bibliographical note

    Copyright of the Massachusetts Institute of Technology Press (MIT Press)

    Keywords

    • regression problem
    • target data
    • Gaussian noise
    • error function
    • noise variance

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  • Cite this

    Bishop, C. M., & Qazaz, C. S. (1997). Regression with input-dependent noise: A Bayesian treatment. In M. C. Mozer, M. I. Jordan, & T. Petsche (Eds.), Advances in Neural Information Processing Systems 9 (Vol. 9, pp. 347-353). (Proceeding of the 1996 conference). MIT.