Active Learning for Optimal Generalization in Trigonometric Polynomial Models

Masashi SUGIYAMA  Hidemitsu OGAWA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.9   pp.2319-2329
Publication Date: 2001/09/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Algorithms and Data Structures
supervised learning,  active learning,  generalization capability,  trigonometric polynomial space,  pseudo orthogonal bases,  

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In this paper, we consider the problem of active learning, and give a necessary and sufficient condition of sample points for the optimal generalization capability. By utilizing the properties of pseudo orthogonal bases, we clarify the mechanism of achieving the optimal generalization capability. We also show that the condition does not only provide the optimal generalization capability but also reduces the computational complexity and memory required to calculate learning result functions. Based on the optimality condition, we give design methods of optimal sample points for trigonometric polynomial models. Finally, the effectiveness of the proposed active learning method is demonstrated through computer simulations.