Abstract
This paper presents learning rates for the least-square regularized regression algorithms with polynomial kernels. The target is the error analysis for the regression problem in learning theory. A regularization scheme is given, which yields sharp learning rates. The rates depend on the dimension of polynomial space and polynomial reproducing kernel Hilbert space measured by covering numbers. Meanwhile, we also establish the direct approximation theorem by Bernstein-Durrmeyer operators in \( L_{\rho _X }^2 \) with Borel probability measure.
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Li, B., Wang, G. Learning rates of least-square regularized regression with polynomial kernels. Sci. China Ser. A-Math. 52, 687–700 (2009). https://doi.org/10.1007/s11425-008-0137-5
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DOI: https://doi.org/10.1007/s11425-008-0137-5
Keywords
- learning theory
- reproducing kernel Hilbert space
- polynomial kernel
- regularization error
- Bernstein-Durrmeyer operators
- covering number
- regularization scheme