Shannon sampling II: Connections to learning theory
Shannon sampling II: Connections to learning theory
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DOI：
10.1016/j.acha.2005.03.001
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发表时间：
2005-11
影响因子：
2.5
通讯作者：
S. Smale;Ding-Xuan Zhou
中科院分区：
文献类型：
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作者：
S. Smale;Ding-Xuan Zhou
我们继续研究[S]。Smale，D. X. Zhou，Shannon sampling and function reconstruction from point values，Bull.Amer.Math.Soc.41（2004）279-305]中所述。本文对误差分析进行了改进。然后，我们展示了我们的方法可以应用于学习理论：一个功能分析框架，维度独立的概率估计，不仅给出了在L2空间中的错误，但也为在再生核希尔伯特空间中的错误，学习算法的执行。覆盖数参数被替换为积分算子的估计。
We continue our study [S. Smale, D.X. Zhou, Shannon sampling and function reconstruction from point values, Bull. Amer. Math. Soc. 41 (2004) 279–305] of Shannon sampling and function reconstruction. In this paper, the error analysis is improved. Then we show how our approach can be applied to learning theory: a functional analysis framework is presented; dimension independent probability estimates are given not only for the error in the L2spaces, but also for the error in the reproducing kernel Hilbert space where the learning algorithm is performed. Covering number arguments are replaced by estimates of integral operators.