%latex file of abstract \begin{slide} \begin{center} Multicategory Classification: The Multicategory Support Vector Machine and the Multichotomous Penalized Likelohood Estimate \end{center} \begin{center} Grace Wahba \end{center} \begin{center} Abstract \end{center} We describe two modern methods for statistical model building and classification, penalized likelihood methods and and support vector machines (SVM's). Both are obtained as solutions to optimization problems in reproducing kernel Hilbert spaces (RKHS). A training set is given, and an algorithm for classifiying future observations is built from it. The ($k$-category) multichotomous penalized likelihood method returns a vector of probabilities $(p_1(t), \cdots p_k(t))$ where $t$ is the attribute vector of the object to be classified. The multicategory support vector vachine returns a classifier vector $(f_1(t), \cdots f_k(t))$ satisfying $\sum_\ell f_{\ell}(t) = 0$, where $max_{\ell}f_{\ell}(t)$ identifies the category. The two category SVM's are very well known, while the multi-category SVM (MSVM) described here, which includes modifications for unequal misclassification costs and unrepresentative training sets, is new. \end{slide} \begin{slide} We describe applications of each method: For penalized likelihood, estimating the 10-year probability of death due to several causes, as a function of several risk factors observed in a demographic study, and for MSVM's, classifying radiance profiles from the MODIS instrument according to clear, water cloud or ice cloud. See also G. Wahba, PNAS,2002 -go back to my home page and the TRLIST for the link. Some computational and tuning issues are noted. \end{slide}