Unified approach to coefficient-based regularized regression ?
In this paper, we consider the coefficient-based regularized least-squares regression problem with the lq l q -regularizer (1?q?2) ( 1 ? q ? 2 ) and data dependent hypothesis spaces. Algorithms in 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 error. 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) 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 q = 1 , which is novel. Finally, our results hold under very general conditions.
data dependent hypothesis spaces learning rates coefficient-based regularization scheme lq l q -regularizer lq l q lq l q l q ?2 ? 2 -empirical covering number ?2 ? 2 ?2 ? 2 ? 2