| Worst-Case Bounds for Gaussian Process Models (2005) | |||||||
Abstract | |||||||
| 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 emph{minimum description length} (MDL) framework. Here, we show precisely how Bayesian Gaussian regression is a minimax strategy. | |||||||
Details der Publikation | |||||||
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