Upper and lower bounds on the learning curve for Gaussian processes

In this paper we introduce and illustrate non-trivial upper and lower bound s on the learning curves for one-dimensional Guassian Processes. The analys is is carried out emphasising the effects induced on the bounds by the smoo thness of the random process described by the Modified Bessel and the Squar ed Exponential covariance functions. We present an explanation of the early , linearly-decreasing behavior of the learning curves and the bounds as wel l as a study of the asymptotic behavior of the curves. The effects of the n oise level and the lengthscale on the tightness of the bounds are also disc ussed.