TUTORIAL - Reproducing Kernel Hilbert Spaces and why they are important.

Grace Wahba
University of Wisconsin
Statistics

We assume no previous knowledge of reproducing kernel Hilbert spaces (rkhs). We discuss the Moore-Aronszajn Theorem which gives a 1:1 correspondence between positive definite functions and rkhs, and note that through this relationship a positive definite function
defines a distance measure with an inner product.
In addition we identify the relationship with
Bayes estimates. After describing several popular classes of rkhs we describe the related optimization problems which estimate functions or vectors via (Tihonov) regularization, where the
regularization term is a norm or semi-norm in rkhs. We note a variety of cost functions, including those resulting in penalized likelihood estimates and support vector machines, and briefly mention the problem of tuning, or, the bias-variance tradeoff in function estimation, which balances fit to the data against complexity
of the solution.


Presentation (PDF File)
Video of Talk (RealPlayer File)

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