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PAC-Bayesian generalisation error bounds for gaussian process classification (2002)
| Content Provider | CiteSeerX |
|---|---|
| Author | Seeger, Matthias |
| Abstract | 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 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. |
| File Format | |
| Journal | Journal of Machine Learning Reasearch |
| Publisher Date | 2002-01-01 |
| Access Restriction | Open |
| Subject Keyword | Interpretable Result Strong Learning-theoretical Justification Vector Machine Gaussian Process Classification Distribution-free Error Bound Distributionfree Generalisation Error Unfavourable Scaling Simple Probabilistic Model Powerful Theorem Pac-bayesian Theorem Powerful Nonparametric Learning Method Pac-bayesian Generalisation Error Moderate Training Sample Size Approximate Bayesian Gpc Method Particular Gpc Technique Approximate Bayesian Gp Classification Technique Recent Sparse Method Approximate Bayesian Gaussian Process Real-world Task Standard Gp Algorithm Convex Duality |
| Content Type | Text |
| Resource Type | Article |
