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Unified approach to coefficient-based regularized regression. (English) Zbl 1228.62044
Summary: We consider the coefficient-based regularized least-squares regression problem with the $$l^{q}$$-regularizer ($$1\leq q\leq 2$$) 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:
 62G08 Nonparametric regression and quantile regression 68T99 Artificial intelligence
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