Approximation by multivariate max-product Kantorovich-type operators and learning rates of least-squares regularized regression

Lucian Coroianu; Danilo Costarelli; Sorin G. Gal; Gianluca Vinti

doi:10.3934/cpaa.2020189

Article Contents

2020, Volume 19, Issue 8: 4213-4225. Doi: 10.3934/cpaa.2020189

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Approximation by multivariate max-product Kantorovich-type operators and learning rates of least-squares regularized regression

1.
Department of Mathematics and Computer Science, University of Oradea, Oradea, Romania
2.
Department of Mathematics and Computer Science, University of Perugia, Perugia, Italy

^* Corresponding author
^* Corresponding author

Received: September 30, 2019

Revised: February 29, 2020

Published: May 2020

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Abstract

In a recent paper, for univariate max-product sampling operators based on general kernels with bounded generalized absolute moments, we have obtained several $ L^{p}_{\mu} $ convergence properties on bounded intervals or on the whole real axis. In this paper, firstly we obtain quantitative estimates with respect to a $ K $-functional, for the multivariate Kantorovich variant of these max-product sampling operators with the integrals written in terms of Borel probability measures. Applications of these approximation results to learning theory are obtained.

Keywords:

Multivariate max-product sampling Kantorovich operators,
Borel probability measures,
multivariate generalized kernels,
L_µ^p-norm,
$ 1\le p <\infty $,
$ K $-functional,
learning theory,
regularizing function,
sample error,
regularized error.

Mathematics Subject Classification: Primary: 41A35, 41A25, 41A63; Secondary: 62J02, 68T05.

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