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Support Vector Machines, Reproducing Kernel Hilbert Spaces and the Randomized Gacv 1 1 Support Vector Machines, Reproducing Kernel Hilbert Spaces and the Randomized Gacv
| Content Provider | Semantic Scholar |
|---|---|
| Author | Wahba, Grace |
| Copyright Year | 1998 |
| Abstract | 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 tensor sums and products of RKHS including smoothing spline ANOVA spaces in the context of SVM's is also described. (2) A discussion of the relationship between penalized likelihood methods in RKHS for Bernoulli data when the goal is risk factor estimation, and SVM methods in RKHS when the goal is classiication. When the goal is classiication it is noted that replacing the likelihood functional of the logit (log odds ratio) with an appropriate SVM functional is a natural method for concentrating computational eeort on estimating the logit near the classiication boundary and ignoring data far away. Remarks concerning the potential of SVM's for variable selection as an eecient preprocessor for risk factor estimation are made. (3) A discussion of how the the GACV (Generalized Approximate Cross Validation) for choosing smoothing parameters proposed in Xiang and Wahba (1996, 1997) may be adapted and implemented in the context of certain convex SVM's. |
| File Format | PDF HTM / HTML |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
