Regularized learning in Banach spaces as an optimization problem: representer theorems |
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Authors: | Haizhang Zhang Jun Zhang |
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Institution: | 1. University of Michigan, Ann Arbor, MI, 48109, USA 2. School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou, 510275, China
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Abstract: | We view regularized learning of a function in a Banach space from its finite samples as an optimization problem. Within the framework of reproducing kernel Banach spaces, we prove the representer theorem for the minimizer of regularized learning schemes with a general loss function and a nondecreasing regularizer. When the loss function and the regularizer are differentiable, a characterization equation for the minimizer is also established. |
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