Probabilistic methods for Support Vector Machines

SVMs can be interpreted as MAP-solutions to inference problems with Gaussian Process priors. The evidence for certain hyperparameter values can then be calculated and used to optimize e.g. C, which cannot be set from cross-validation/test error alone; error bars can also be obtained. I show how this helps with the intuitive interpretation of SVM kernels; it also allows Bayesian methods to be used for SVMs (tuning hyper-parameters by maximizing evidence, defining error bars etc).