General Bounds on Bayes Errors for Regression with Gaussian Processes

Part of Advances in Neural Information Processing Systems 11 (NIPS 1998)

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Manfred Opper, Francesco Vivarelli


Based on a simple convexity lemma, we develop bounds for differ(cid:173) ent 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 distri(cid:173) bution which equals the weight function of the covariance kernel, yielding asymptotically tight results. The results are compared with numerical experiments.