Learning rates of least-square regularized regression
Learning rates of least-square regularized regression
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DOI：
10.1007/s10208-004-0155-9
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发表时间：
2006-05-01
影响因子：
3
通讯作者：
Zhou, Ding-Xuan
中科院分区：
文献类型：
--
作者：
Wu, Qiang;Ying, Yiming;Zhou, Ding-Xuan
本文考虑了与最小平方损失和再生核Hilbert空间相关的正则化学习算法。目标是学习理论中回归问题的误差分析。提出了一种新的正则化方法，它产生了令人满意的学习率。速率依赖于逼近性质和再生核Hilbert空间的覆盖数度量的容量。当核是C-无穷大并且回归函数位于相应的再生核希尔伯特空间中时，速率是m（-zeta），zeta任意接近1，而不管有界概率分布的方差如何。
This paper considers the regularized learning algorithm associated with the least-square loss and reproducing kernel Hilbert spaces. The target is the error analysis for the regression problem in learning theory. A novel regularization approach is presented, which yields satisfactory learning rates. The rates depend on the approximation property and on the capacity of the reproducing kernel Hilbert space measured by covering numbers. When the kernel is C-infinity and the regression function lies in the corresponding reproducing kernel Hilbert space, the rate is m(-zeta) with zeta arbitrarily close to 1, regardless of the variance of the bounded probability distribution.