General bounds on Bayes errors for regression with Gaussian processes

Manfred Opper, Francesco Vivarelli

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Based on a simple convexity lemma, we develop bounds for different types of Bayesian prediction errors for regression with Gaussian processes. The basic bounds are formulated for a fixed training set. Simpler expressions are obtained for sampling from an input distribution which equals the weight function of the covariance kernel, yielding asymptotically tight results. The results are compared with numerical experiments.

    Original languageEnglish
    Title of host publicationAdvances in Neural Information Processing Systems 1999
    Pages302-308
    Number of pages7
    Publication statusPublished - 1999
    Event12th Annual Conference on Neural Information Processing Systems, NIPS 1998 - Denver, CO, United Kingdom
    Duration: 30 Nov 19985 Dec 1998

    Conference

    Conference12th Annual Conference on Neural Information Processing Systems, NIPS 1998
    CountryUnited Kingdom
    CityDenver, CO
    Period30/11/985/12/98

    Fingerprint

    Sampling
    Experiments

    Bibliographical note

    Copyright of the Massachusetts Institute of Technology Press (MIT)

    Keywords

    • convexity
    • Bayesian prediction errors
    • regression
    • Gaussian processes
    • covariance kernel
    • asymptotically

    Cite this

    Opper, M., & Vivarelli, F. (1999). General bounds on Bayes errors for regression with Gaussian processes. In Advances in Neural Information Processing Systems 1999 (pp. 302-308)
    Opper, Manfred ; Vivarelli, Francesco. / General bounds on Bayes errors for regression with Gaussian processes. Advances in Neural Information Processing Systems 1999. 1999. pp. 302-308
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    Opper, M & Vivarelli, F 1999, General bounds on Bayes errors for regression with Gaussian processes. in Advances in Neural Information Processing Systems 1999. pp. 302-308, 12th Annual Conference on Neural Information Processing Systems, NIPS 1998, Denver, CO, United Kingdom, 30/11/98.

    General bounds on Bayes errors for regression with Gaussian processes. / Opper, Manfred; Vivarelli, Francesco.

    Advances in Neural Information Processing Systems 1999. 1999. p. 302-308.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

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    Opper M, Vivarelli F. General bounds on Bayes errors for regression with Gaussian processes. In Advances in Neural Information Processing Systems 1999. 1999. p. 302-308