Statistical Inference with Reproducing Kernel Hilbert Space

2008, Statistical Learning Theory II
The Graduate University for Advanced Studies, ISM

Lecturer: Kenji Fukumizu(Institute of Statistical Mathematics)

Schedule: April.18 - Friday, 10:30-12:00

Place: (253(B) Kensyuu-shitsu, 2F)

Class schedule

We have class on April 18, 25, May 2, 9, 23, 30, June 13, 20, 27. July 25, September 12, 26
No class on May 16, June 6, July 4, 11, 18.

Purpose of course

An introduction to the methodology of statistical inferrence with positive definite kernels or reproducing kernel Hilbert spaces. The course explains the basic ideas of the methods with explanation of necessary mathematical background. Various kernel methods are explained, with special focus on SVM. Also, recent development of dependence anlaysis with kernels are explained in detail.

Plan of lectures

0. Outline and Information on the course (slides)

1. Introduction: overview of kernel methods (slides)

2. Elements of positive definite kernel and reproducing kernel Hilbert space (slides)

3. Methods with kernels (slides)

4. Support vector machines I (slides)

5. Support vector machines II (slides)

6. Generalization ability of SVM (slides)

7. Theory of positive definite kernel and reproducing kernel Hilbert space (slides)

8. Mean Element in RKHS (slides)

9. Dependence analysis with kernels (slides)

10. Various aspects of kernel methods (slides)



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