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

JOURNAL OF APPROXIMATION THEORY

卷:173

Article

Li, Bing-Zheng

关键词: Approximation;    Learning theory;    Reproducing kernel Hilbert space;    Polynomial kernel;    Regularization error;    Bernstein-Durrmeyer operators;    Covering number;    Regularization scheme;   

DOI  :  10.1016/j.jat.2013.04.007

来源: Elsevier

【 摘 要 】

In this paper, we establish error bounds for approximation by multivariate Bernstein-Durrmeyer operators in L-rho X(p) (1 <= p < infinity) with respect to a general Borel probability measure rho x on a simplex X subset of R-n. By the error bounds, we provide convergence rates of type O (m(-gamma)) with some gamma > 0 for the least-squares. regularized regression algorithm associated with a multivariate polynomial kernel (where in is the sample size). The learning rates depend on the space dimension a and the capacity of the reproducing kernel Hilbert space generated by the polynomial kernel. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free