Upper and lower bounds on the learning curve for Gaussian processes

Christopher K. I. Williams, Francesco Vivarelli

    Research output: Contribution to journalArticlepeer-review


    In this paper we introduce and illustrate non-trivial upper and lower bounds on the learning curves for one-dimensional Gaussian Processes. The analysis is carried out emphasising the effects induced on the bounds by the smoothness of the random process described by the Modified Bessel and the Squared Exponential covariance functions. We present an explanation of the early, linearly-decreasing behavior of the learning curves and the bounds as well as a study of the asymptotic behavior of the curves. The effects of the noise level and the lengthscale on the tightness of the bounds are also discussed.

    Original languageEnglish
    Pages (from-to)77-102
    Number of pages26
    JournalMachine Learning
    Issue number1
    Publication statusPublished - Jul 2000


    • non-trivial
    • Gaussian Processes
    • modified Bessel
    • covariance functions
    • learning curves


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