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Based on a statistical mechanics approach, we develop a method for approximately computing average case learning curves for Gaus-sian process regression models. The approximation works well in the large sample size limit and for arbitrary dimensionality of the input space. We explain how the approximation can be systematically improved and argue that(More)
Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica " trick " of statistical physics and the TAP approach for approximate Bayesian inference. We demonstrate our approach on(More)
We employ the replica method of statistical physics to study the average case performance of learning systems. The new feature of our theory is that general distributions of data can be treated, which enables applications to real data. For a class of Bayesian prediction models which are based on Gaussian processes, we discuss Bootstrap estimates for(More)
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