Support Vector Machines (SVMs) can be interpreted as maximum a posteriori solutions to inference problems with Gaussian Process (GP) priors and appropriate likelihood functions. Focussing on the case of classification, I show first that such aninterpretation gives a clear intuitive meaning to SVM kernels, as covariance functions of GP priors; this can be used to guide the choice of kernel. Second, a probabilistic interpretation allows Bayesian methods to be used for SVMs: Using a localapproximation of the posterior around its maximum (the standard SVM solution), I discuss 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.
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