Optimal learning rates for least squares regularized regression with unbounded sampling
Optimal learning rates for least squares regularized regression with unbounded sampling
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DOI：
10.1016/j.jco.2010.10.002
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发表时间：
2011-02-01
影响因子：
1.7
通讯作者：
Zhou, Ding-Xuan
中科院分区：
文献类型：
--
作者：
Wang, Cheng;Zhou, Ding-Xuan
回归学习算法理论研究的一个标准假设是输出样本值的一致有界性。这排除了高斯噪声的常见情况。本文研究了再生核Hilbert空间中最小二乘正则化方法产生的回归的学习算法，该算法不需要样本的一致有界性假设。通过在输出变量的矩上施加一些增量条件，我们根据回归函数的正则性和假设空间的容量来推导学习率。我们的分析的新颖性是一种新的覆盖数论元，用于界定样本误差。(C)2010 Elsevier Inc.保留所有权利。
A standard assumption in theoretical study of learning algorithms for regression is uniform boundedness of output sample values. This excludes the common case with Gaussian noise. In this paper we investigate the learning algorithm for regression generated by the least squares regularization scheme in reproducing kernel Hilbert spaces without the assumption of uniform boundedness for sampling. By imposing some incremental conditions on moments of the output variable, we derive learning rates in terms of regularity of the regression function and capacity of the hypothesis space. The novelty of our analysis is a new covering number argument for bounding the sample error. (c) 2010 Elsevier Inc. All rights reserved.