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Abstract : |
Approximate Bayesian Gaussian process (GP) classication techniques are powerful nonparametric learning methods, similar in appearance and performance to Support Vector machines. Based on simple probabilistic models, they render interpretable results and can be embedded in Bayesian frameworks for model selection, feature selection, etc. In this paper, by applying the PAC-Bayesian theorem of McAllester (1999), we prove distributionfree generalization error bounds for a wide range of approximate Bayesian GP classication techniques. We instantiate and test these bounds for two particular GPC techniques, including a sparse method which circumvents the unfavourable scaling of standard GP algorithms. As is shown in experiments on a real-world task, the bounds can be very tight for moderate training sample sizes. To the best of our knowledge, these results provide the tightest known distribution-free error bounds for approximate Bayesian GPC methods, giving a strong learning-theoretical justication for the use of these techniques., |
