document: Shrinkage estimator generalizations of Proximal Support Vector Machines We give a statistical interpretation of Proximal Support Vector Machines ( PSVM ) proposed at KDD2001 as linear approximaters to ( nonlinear ) Support Vector Machines ( SVM ) . We prove that PSVM using a linear kernel is identical to ridge regression , a biased-regression method known in the statistical community for more than thirty years . Techniques from the statistical literature to estimate the tuning constant that appears in the SVM and PSVM framework are discussed . Better shrinkage strategies that incorporate more than one tuning constant are suggested . For nonlinear kernels , the minimization problem posed in the PSVM framework is equivalent to finding the posterior mode of a Bayesian model defined through a Gaussian process on the predictor space . Apart from providing new insights , these interpretations help us attach an estimate of uncertainty to our predictions and enable us to build richer classes of models . In particular , we propose a new algorithm called PSVMMIX which is a combination of ridge regression and a Gaussian process model . Extension to the case of continuous response is straightforward and illustrated with example datasets .
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