Probabilistic interpretations and Bayesian methods for support vector machines

Support vector machines (SVMs) can be interpreted as maximum a posteriori solutions to inference problems with Gaussian process priors and appropriate likelihood functions. Focusing on the case of classification, the author shows first that such an interpretation gives a clear intuitive meaning to SVM kernels, as covariance functions of GP priors; this can be used to guide the choice of kernel. Next, a probabilistic interpretation allows Bayesian methods to be used for SVMs. Using a local approximation of the posterior around its maximum (the standard SVM solution), he discusses how the evidence for a given kernel and noise parameter can be estimated, and how approximate error bars for the classification of test points can be calculated