PAC-Bayesian Generalisation 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 McAllester (1999a), we prove distributionfree generalisation error bounds for a wide range of approximate Bayesian GP classification techniques. We also provide a new and much simplified proof for this powerful theorem, making use of the concept of convex duality which is a backbone of many machine learning techniques. We instantiate and test our bounds for two particular GPC techniques, including a recent 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 siz...

• Type: Journal
• Year: 2002
• Where: JMLR
• Authors: Matthias Seeger
• Keywords: Approximate Bayesian Gp, Bayesian Gaussian Process, JMLR 2002, Simple Probabilistic Models