Optimal rules with polynomial precision for Hilbert spaces possessing reproducing kernel functions

1975 ◽  
Vol 25 (4) ◽  
pp. 379-382 ◽  
Author(s):  
M. M. Chawla ◽  
Veena Kaul
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Kernel Functions

INDEFINITE KERNEL NETWORK WITH DEPENDENT SAMPLING

2013 ◽  
Vol 11 (05) ◽  
pp. 1350020 ◽  
Author(s):  
HONGWEI SUN ◽  
QIANG WU
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Function Class ◽  
Positive Definiteness ◽  
Reproducing Kernel Hilbert Spaces ◽  
Strong Mixing ◽  
Mixing Condition ◽  
Indefinite Kernel ◽  
Learning Rates ◽  
Kernel Hilbert Spaces

We study the asymptotical properties of indefinite kernel network with coefficient regularization and dependent sampling. The framework under investigation is different from classical kernel learning. Positive definiteness is not required by the kernel function and the samples are allowed to be weakly dependent with the dependence measured by a strong mixing condition. By a new kernel decomposition technique introduced in [27], two reproducing kernel Hilbert spaces and their associated kernel integral operators are used to characterize the properties and learnability of the hypothesis function class. Capacity independent error bounds and learning rates are deduced.

scholarly journals Scattering Systems with Several Evolutions and Formal Reproducing Kernel Hilbert Spaces

2014 ◽  
Vol 9 (4) ◽  
pp. 827-931 ◽  
Author(s):  
Joseph A. Ball ◽  
Dmitry S. Kaliuzhnyi-Verbovetskyi ◽  
Cora Sadosky ◽  
Victor Vinnikov
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Spaces ◽  
Kernel Hilbert Spaces ◽  
Scattering Systems
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