PAC-Bayesian Generalization Error Bounds for Gaussian Process Classification

Approximate Bayesian Gaussian process (GP) classification 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 ncitemcallester:99, we prove distribution-free generalization error bounds for a wide range of approximate Bayesian GP classification 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 justification for the use of these techniques.