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

作者：Li, Bing-Zheng^*

来源：Journal of Approximation Theory, 2013, 173: 33-55.

DOI：10.1016/j.jat.2013.04.007

• Approximation
• Learning theory
• Reproducing kernel Hilbert space
• Polynomial kernel
• Regularization error
• Bernstein-Durrmeyer operators
• Covering number
• Regularization scheme

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.

• 出版日期2013-9
• 单位浙江大学