We review the two category support vector machine and two-category penalized likelihood estimates, and note that both implement the Bayes rule (sign of the log-odds ratio in the "standard" case) if tuned optimally, but the support vector machine estimates the sign directly while the penalized likelihood estimate estimates the log-odds ratio itself, and hence a probability estimate.Then we describe generalizations of these two approaches to the multicategory case, focusing on the MSVM of Lee, Lin and Wahba and a neralization of the two category penalized likelihood case originally due to X. Lin. Recent applications will be described, and remarks on the relative merits of SVM's and penalized likelihood estimates in different problems will be made.
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