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Two-category support vector machines (SVM) have been very popular in the machine learning community for classii cation problems. Solving multicategory problems by a series of binary classii ers is quite common in the SVM paradigm; however, this approach may fail under various circumstances. We propose the multicategory support vector machine (MSVM), which(More)
In this paper, we propose a Generalized Approximate Cross Validation (GACV) function for estimating the smoothing parameter in the penalized log likelihood regression problem with non-Gaussian data. This GACV is obtained by, first, obtaining an approximation to the leaving-out-one function based on the negative log likelihood, and then, in a step(More)
The Support Vector Machine (SVM) has shown great performance in practice as a classification methodology. Oftentimes multicategory problems have been treated as a series of binary problems in the SVM paradigm. Even though the SVM implements the optimal classification rule asymptotically in the binary case, solutions to a series of binary problems may not be(More)
The majority of classification algorithms are developed for the standard situation in which it is assumed that the examples in the training set come from the same distribution as that of the target population, and that the cost of misclassification into different classes are the same. However, these assumptions are often violated in real world settings. For(More)
The LASSO-Patternsearch algorithm is proposed to efficiently identify patterns of multiple dichotomous risk factors for outcomes of interest in demographic and genomic studies. The patterns considered are those that arise naturally from the log linear expansion of the multivariate Bernoulli density. The method is designed for the case where there is a(More)
Reproducing kernel Hilbert space (RKHS) methods provide a unified context for solving a wide variety of statistical modelling and function estimation problems. We consider two such problems: We are given a training set [yi, ti, i = 1, em leader, n], where yi is the response for the ith subject, and ti is a vector of attributes for this subject. The value of(More)
We develop and apply a previously undescribed framework that is designed to extract information in the form of a positive definite kernel matrix from possibly crude, noisy, incomplete, inconsistent dissimilarity information between pairs of objects, obtainable in a variety of contexts. Any positive definite kernel defines a consistent set of distances, and(More)
We combine a smoothing spline analysis of variance (SS-ANOVA) model and a log-linear model to build a partly exible model for multivariate Bernoulli data. The joint distribution conditioning on the predictor variables is estimated. The log odds ratio is used to measure the association between outcome variables. A numerical scheme based on the block one-step(More)
We propose the randomized Generalized Approximate Cross Validation (ranGACV) method for choosing multiple smoothing parameters in penalized likelihood estimates for Bernoulli data. The method is intended for application with penalized likelihood smoothing spline ANOVA models. In addition we propose a class of approximate numerical methods for solving the(More)