Probabilistic methods for Support Vector Machines

I describe a framework for interpreting Support Vector Machines (SVMs) as maximum a posteriori (MAP) solutions to inference problems with Gaussian Process priors. This can provide intuitive guidelines for choosing a 'good' SVM kernel. It can also assign (by evidence maximization) optimal values to parameters such as the noise level C which cannot be determined unambiguously from properties of the MAP solution alone (such as cross-validation error). I illustrate this using a simple approximate expression for the SVM evidence. Once C has been determined, error bars on SVM predictions can also be obtained.