Regularized learning in Banach spaces as an optimization problem: representer theorems
Regularized learning in Banach spaces as an optimization problem: representer theorems
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DOI：
10.1007/s10898-010-9575-z
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发表时间：
2010-07
影响因子：
1.8
通讯作者：
Haizhang Zhang;Jun Zhang
中科院分区：
文献类型：
--
作者：
Haizhang Zhang;Jun Zhang
我们将Banach空间中函数从其有限样本中的正则化学习视为一个最优化问题。在再生核Banach空间的框架下，我们证明了具有一般损失函数和非递减正则化函数的正则化学习方案的最小化的表示定理。当损失函数和正则化函数可微时，还建立了极小化的特征方程。
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.