Statistical Data Analysis with Positive Definite Kernels

Lecturer: Kenji Fukumizu (Institute of Statistical Mathematics)

Schedule: October.6 - 10, 2008

Place: Kyushu University

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.

Report

Problems
Deadline: November 10 (Mon.)

Plan of lectures

Slides of the lectures

1. Introduction to kernel methods. slides

2. Elements of positive definite kernels and RKHS. slides

3. Various methods with kernels. slides

4. Support vector machine I. slides

5. Support vector machine II. slides

6. Theory on positive definite kernels. slides

7. Mean on RKHS and characteristic property. slides

8. Dependence with kernels. slides

9. Relation to smoothing spline. slides

References

Learning with Kernels. B.Schoelkopf and A.Smola. (2001) MIT Press.
An Introduction to Support Vector Machines and Other Kernel-based Learning Methods. N.Cristianini and J.Shawe-Taylor (2000) Cambridge University Press.

Evaluation

Report topics will be assgined during the course.

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