How to design a regularization term for improving generalization

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In supervised learning, the regularization method is often used for improving the level of generalization. We give a necessary and sufficient condition of an optimal regularization term, i.e., a regularization operator and parameter. The optimality is discussed based on the projection learning criterion in which the minimization of a generalization error is explicitly considered. We suggest how to design the optimal regularization term so as to satisfy the obtained condition.

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