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Bayesian methods for support vector machines: Evidence and predictive class probabilities
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DOI：10.1023/A:1012489924661.png)
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摘要
En 中文
I describe a framework for interpreting Support Vector Machines (SVMs) as maximum a posteriori (MAP) solutions to inference problems with Gaussian Process priors. This probabilistic interpretation can provide intuitive guidelines for choosing a 'good' SVM kernel. Beyond this, it allows Bayesian methods to be used for tackling two of the outstanding challenges in SVM classification: how to tune hyperparameters-the misclassification penalty C, and any parameters specifying the ernel-and how to obtain predictive class probabilities rather than the conventional deterministic class label predictions. Hyperparameters can be set by maximizing the evidence; I explain how the latter can be defined and properly normalized. Both analytical approximations and numerical methods (Monte Carlo chaining) for estimating the evidence are discussed. I also compare different methods of estimating class probabilities, ranging from simple evaluation at the MAP or at the posterior average to full averaging over the posterior. A simple toy application illustrates the various concepts and techniques.
Keyword:
Support vector machines
Gaussian processes
Bayesian inference
evidence
hyperparameter tuning
probabilistic predictions
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