Nonparametric estimation and classification using radial basis function nets and empirical risk minimization
Nonparametric estimation and classification using radial basis function nets and empirical risk minimization
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DOI：
10.1109/72.485681
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发表时间：
1996-03-01
影响因子：
--
通讯作者：
Lugosi, G
中科院分区：
文献类型：
--
作者：
Krzyzak, A;Linder, T;Lugosi, G
本文研究了一类基函数的径向基函数（RBF）网络的收敛性，并对相关的方法和结果进行了综述。我们通过经验风险最小化来获得网络参数。在非线性函数逼近问题和非参数分类问题中，我们证明了最优网络是一致的。对于分类问题，我们考虑了两种方法：通过非线性函数估计选择RBF分类器和最小化经验误差概率的直接方法。分析中使用的工具包括无分布的非渐近概率不等式和涵盖函数类的数。
In this paper we study convergence properties of radial basis function (RBF) networks for a large class of basis functions, and review the methods and results related to this topic. We obtain the network parameters through empirical risk minimization. We show the optimal nets to be consistent in the problem of nonlinear function approximation and in nonparametric classification. For the classification problem we consider two approaches: the selection of the RBF classifier via nonlinear function estimation and the direct method of minimizing the empirical error probability. The tools used in the analysis include distribution-free nonasymptotic probability inequalities and covering numbers for classes of functions.