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Conference Paper

Worst-Case Bounds for Gaussian Process Models


Seeger,  M
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Kakade, S., Seeger, M., & Foster, D. (2006). Worst-Case Bounds for Gaussian Process Models. Advances in Neural Information Processing Systems 18: Proceedings of the 2005 Conference, 619-626.

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We present a competitive analysis of some non-parametric Bayesian algorithms in a worst-case online learning setting, where no probabilistic assumptions about the generation of the data are made. We consider models which use a Gaussian process prior (over the space of all functions) and provide bounds on the regret (under the log loss) for commonly used non-parametric Bayesian algorithms - including Gaussian regression and logistic regression - which show how these algorithms can perform favorably under rather general conditions. These bounds explicitly handle the infinite dimensionality of these non-parametric classes in a natural way. We also make formal connections to the minimax and emphminimum description length (MDL) framework. Here, we show precisely how Bayesian Gaussian regression is a minimax strategy.