Training Data Selection for Optimal Generalization in Trigonometric Polynomial Networks
Masashi Sugiyama, Hidemitsu Ogawa · 1999
In this paper, we consider the problem of active learning in trigonometric polynomial networks and give a necessary and su#cient condition of sample points to provide the optimal generalization capability. By analyzing the condition from the functional analytic point of view, we clarify the mechanism of achieving the optimal generalization capability. We also show that a set of training examples satisfying the condition does not only provide the optimal generalization but also reduces the computational complexity and memory required for the calculation of learning results. Finally, examples of sample points satisfying the condition are given and computer simulations are performed to demonstrate the e#ectiveness of the proposed active learning method. 1 Introduction Supervised learning is obtaining an underlying rule from training examples, and can be formulated as a function approximation problem. If sample points are actively designed, then learning can be performed more e#ciently. I...