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Motivated by the Golub–Heath–Wahba formula for ridge regression, we first present a new leave-one-out lemma for the kernel support vector machines (SVM) and related large-margin classifiers. We then use the lemma to design a novel and efficient algorithm, named “magicsvm,” for training the kernel SVM and related large-margin classifiers and computing the exact leave-one-out cross-validation error. By “magicsvm,” the computational cost of leave-one-out analysis is of the same order of fitting a single SVM on the training data. We show that “magicsvm” is much faster than the state-of-the-art SVM solvers based on extensive simulations and benchmark examples. The same idea is also used to boost the computation speed of the  V -fold cross-validation of the kernel classifiers.

Fast and Exact Leave-One-Out Analysis of Large-Margin Classifiers