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Zbl 1228.62044
Feng, Yun-Long; Lv, Shao-Gao
Unified approach to coefficient-based regularized regression.
(English)
[J] Comput. Math. Appl. 62, No. 1, 506-515 (2011). ISSN 0898-1221

Summary: We consider the coefficient-based regularized least-squares regression problem with the $l^{q}$-regularizer ($1\le q\le 2$) and data dependent hypothesis spaces. Algorithms for data dependent hypothesis spaces perform well with the property of flexibility. We conduct a unified error analysis by a stepping stone technique. An empirical covering number technique is also employed in our study to improve sample errors. Comparing with existing results, we make a few improvements: First, we obtain a significantly sharper learning rate that can be arbitrarily close to $O(m^{ - 1})$ under reasonable conditions, which is regarded as the best learning rate in learning theory. Second, our results cover the case $q=1$, which is novel. Finally, our results hold under very general conditions.
MSC 2000:
*62G08 Nonparametric regression
68T99 Artificial intelligence

Keywords: data dependent hypothesis spaces; $l^{q}$-regularizer; $\ell ^{2}$-empirical covering number; learning rates

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