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The convergence rates of Shannon sampling learning algorithms

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Science China Mathematics 2012年第6期55卷 1243-1256页

作者： sheng baohuai Department of Mathematics Shaoxing College of Arts and SciencesShaoxing 312000China

In the present paper,we provide an error bound for the learning rates of the regularized Shannon sampling learning scheme when the hypothesis space is a reproducing kernel Hilbert space(RKHS) derived by a Mercer kernel and a determined *** show that if the sample is taken according to the determined set,then,the sample error can be bounded by the Mercer matrix with respect to the samples and the determined *** regularization error may be bounded by the approximation order of the reproducing kernel Hilbert space interpolation *** paper is an investigation on a remark provided by Smale and Zhou.

关键词： function reconstruction reproducing kernel Hilbert spaces Shannon sampling learning algorithm learning theory sample error regularization error

Error Analysis on Hérmite Learning with Gradient Data

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Chinese Annals of Mathematics,Series B 2018年第4期39卷 705-720页

作者： baohuai sheng Jianli WANG Daohong XIANG Department of Mathematics Shaoxing Univeristy Shaoxing 312000 Zhejiang China. Department of Mathematics Zhejiang Normal University Jinhua 321004 Zhejiang China.

This paper deals with Hermite learning which aims at obtaining the target function from the samples of function values and the gradient values. Error analysis is conducted for these algorithms by means of approaches f... 详细信息

关键词： Hermite learning Gradient learning Learning rate Convex analysis Multitask learning Differentiable reproducing kernel Hilbert space

LEARNING RATES OF KERNEL-BASED ROBUST CLASSIFICATION

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Acta Mathematica Scientia 2022年第3期42卷 1173-1190页

作者： Shuhua WANG baohuai sheng School of Information Engineering Jingdezhen Ceramic UniversityJingdezhen 333403China Department of Finance Zhejiang Yuexiu UniversityShaoxing 312030China Department of Applied Statistics Shaoxing UniversityShaoxing 312000China

This paper considers a robust kernel regularized classification algorithm with a non-convex loss function which is proposed to alleviate the performance deterioration caused by the outliers.A comparison relationship between the excess misclassification error and the excess generalization error is provided;from this,along with the convex analysis theory,a kind of learning rate is *** results show that the performance of the classifier is effected by the outliers,and the extent of impact can be controlled by choosing the homotopy parameters properly.

关键词： Support vector machine robust classification quasiconvex loss function learning rate right-sided directional derivative

A WAY OF CONSTRUCTING TRANSLATION NETWORK OPERATORS BY BERNSTEIN OPERATORS

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Analysis in Theory and Applications 2006年第4期22卷 319-328页

作者： baohuai sheng Shaoxing University China Department of MathematicsShaoxing University Shaoxing 312000 Zhejiang P. R. China

In the present paper, we provide a way of constructing translation network operators by BernsteinDurrmeyer operators.

关键词： Bernstein operator translation network approximation

AN APPLICATION OF BERNSTEIN-DURRMEYER OPERATORS

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Analysis in Theory and Applications 2007年第1期23卷 16-25页

作者： baohuai sheng Chunping Zhang Department of Mathematics Shaoxing College of Arts and Sciences Shaoxing Zhejiang 312000 P. R. China Department of Mathematics Ningbo University Ningbo Zhejiang 315211 P. R. China

In the present paper, we find that the Bernstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help of the de la Vallée properties of the Bernstein-Durrmeyer operators a sequence of translation network operators is constructed and its degree of approximation is dealt.

关键词： Bernstein-Durrmeyer operator translation network approximation

APPLICATIONS OF BERNSTEIN-DURRMEYER OPERATORS IN ESTIMATING THE COVERING NUMBER

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Analysis in Theory and Applications 2010年第2期26卷 186-200页

作者： Chunping Zhang Jianli Wang baohuai sheng Zhejiang Industry Polytechnic College China Shaoxing College of Arts and Sciences China

The paper deals with estimates of the covering number for some Mercer kernel Hilbert space with Bernstein-Durrmeyer operators. We first give estimates of l2- norm of Mercer kernel matrices reproducing by the kernelsK（α,β）（x,y）：=∑∞k=0 Ck（α,β）（x）Qk（α,β）（y）,where Qk（α,β）（x） are the Jacobi polynomials of order k on （0, 1 ）, Ck（α,β）〉 0 are real numbers, and from which give the lower and upper bounds of the covering number for some particular reproducing kernel Hilbert space reproduced by Kα,β （x, y）.

关键词： Mercer kernel matrix covering number Bernstein-Durrmeyer operator

APPLICATIONS OF THE BERNSTEIN-DURRMEYER OPERATORS IN ESTIMATING THE NORM OF MERCER KERNEL MATRICES

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Analysis in Theory and Applications 2008年第1期24卷 74-86页

作者： Chunping Zhang baohuai sheng Zhixiang Chen Ningbo University China Shaoxing College of Arts and Sciences China

The paper is related to the norm estimate of Mercer kernel matrices. The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on [0, 1] × [0, 1] based on the Bernstein-Durrmeyer operator kernel are obtained, with which and the approximation property of the Bernstein-Durrmeyer operator the lower and upper bounds of the Rayleigh entropy number and the l2 -norm for general Mercer kernel matrices on [0, 1] x [0, 1] are provided.

关键词： Mercer kernel matrix Rayleigh entropy number Bernstein-Durrmeyer operator

Solving Neumann Boundary Problem with Kernel-Regularized Learning Approach

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Journal of Applied Mathematics and Physics 2024年第4期12卷 1101-1125页

作者： Xuexue Ran baohuai sheng Department of Mathematics Shaoxing University Shaoxing China

We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.

关键词： Neumann Boundary Value Kernel-Regularized Approach Reproducing Kernel Hilbert Space The Unit Ball The Unit Sphere

THE MARCINKIEWICZ -ZYGMUND INEQUALITYIN Ba SPACES (I)

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Journal of Systems Science & Complexity 2003年第1期16卷 74-84页

作者： sheng baohuai LIU Sanyang CHEN Guangrong Institute of Mathematics Ningbo University Ningbo Zhejiang 315211 China

The Marcinkiewicz-Zygmund inequality with derivative for an algebraic polynomial of order < N = (q + 1)n - 1 is established in a Ba space. As a corollary, the Marcinkiewicz-Zygmund inequality with derivative for an al... 详细信息

关键词： Marcinkiewicz-Zygmund inequality Ba spaces Orlicz spaces.