Full length article: Approximation by multivariate Bernstein-Durrmeyer operators and learning rates of least-squares regularized regression with multivariate polynomial kernels

Authors:
Bing-Zheng Li
Affiliations:
-
Venue:
Journal of Approximation Theory
Year:
2013

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Cited 0

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Abstract

In this paper, we establish error bounds for approximation by multivariate Bernstein-Durrmeyer operators in L"@r"""X^p (1@?p0 for the least-squares regularized regression algorithm associated with a multivariate polynomial kernel (where m is the sample size). The learning rates depend on the space dimension n and the capacity of the reproducing kernel Hilbert space generated by the polynomial kernel.