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 er(cid:173) ror) . 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. Support Vector Machines (SVMs) have recently been the subject of intense re(cid:173) search activity within the neural networks community; for tutorial introductions and overviews of recent developments see [1, 2, 3].