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I t is shown how to choose the smoothing parameter when a smoothing periodic spline of degree 2m -1 is used to reconstruct a smooth periodic curve from noisy ordinate data. The noise is assumed "white" , and the true curve is assumed to be in the Sobolev space W,(*ra) of periodic functions with absolutely continuous v-th derivative, v = 0, t . . . . . 2 m I(More)
Two category Support Vector Machines (SVM) have been very popular in the machine learning community for the classification problem. Solving multicategory problems by a series of binary classifiers is quite common in the SVM paradigm. However, this approach may fail under a variety of circumstances. We have proposed the Multicategory Support Vector Machine(More)
This chapter is an expanded version of a talk presented in the NIPS 97 Workshop on Support Vector Machines. It consists of three parts: (1) A brief review of some old but relevant results on constrained optimization in Reproducing Kernel Hilbert Spaces (RKHS), and a review of the relationship between zero-mean Gaussian processes and RKHS. Application of(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)
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 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)
An adaptive spline method for smoothing is proposed which combines features from both regression spline and smoothing spline approaches One of its advantages is the ability to vary the amount of smoothing in response to the inhomogeneous curvature of true functions at di erent locations This method can be applied to many multivariate function estimation(More)
We describe Likelihood Basis Pursuit, a nonparametric method for variable selection and model building, based on merging ideas from Lasso and Basis Pursuit works and from smoothing spline ANOVA models. An application to nonparametric variable selection for risk factor modeling in the Wisconsin Epidemiological Study of Diabetic Retinopathy is described.(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)