Learnability in Hilbert Spaces with Reproducing Kernels
نویسندگان
چکیده
منابع مشابه
Radial kernels and their reproducing kernel Hilbert spaces
We describe how to use Schoenberg’s theorem for a radial kernel combined with existing bounds on the approximation error functions for Gaussian kernels to obtain a bound on the approximation error function for the radial kernel. The result is applied to the exponential kernel and Student’s kernel. To establish these results we develop a general theory regarding mixtures of kernels. We analyze t...
متن کاملReproducing Kernels for Hilbert Spaces of Real Harmonic Functions
This paper studies a family of Hilbert spaces of real harmonic functions on bounded regions in Rn and will show that, for a range of values of s, they are reproducing kernel Hilbert spaces. The spaces are characterized by their boundary traces and the inner products are defined via their expansions in the harmonic Steklov eigenfunctions of the region. The reproducing kernels will then be descri...
متن کاملReal reproducing kernel Hilbert spaces
P (α) = C(α, F (x, y)) = αF (x, x) + 2αF (x, y) + F (x, y)F (y, y), which is ≥ 0. In the case F (x, x) = 0, the fact that P ≥ 0 implies that F (x, y) = 0. In the case F (x, y) 6= 0, P (α) is a quadratic polynomial and because P ≥ 0 it follows that the discriminant of P is ≤ 0: 4F (x, y) − 4 · F (x, x) · F (x, y)F (y, y) ≤ 0. That is, F (x, y) ≤ F (x, y)F (x, x)F (y, y), and this implies that F ...
متن کاملBayesian Learning in Reproducing Kernel Hilbert Spaces
Support Vector Machines nd the hypothesis that corresponds to the centre of the largest hypersphere that can be placed inside version space, i.e. the space of all consistent hypotheses given a training set. The boundaries of version space touched by this hypersphere de ne the support vectors. An even more promising approach is to construct the hypothesis using the whole of version space. This i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2002
ISSN: 0885-064X
DOI: 10.1006/jcom.2001.0586