Active Learning for Optimal Generalization in Trigonometric Polynomial Models
Masashi Sugiyama, Hidemitsu Ogawa · 2001
In this paper, we consider the problem of active learning, and give a necessary and su#cient 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 for calculating learning result functions. Based on the optimality condition, we give design methods of optimal sample points for trigonometric polynomial models. Finally, the e#ectiveness of the proposed active learning method is demonstrated through computer simulations. Keywords machine learning, supervised learning, active learning, generalization capability, trigonometric polynomial space, pseudo orthogonal bases. Active Learning for Optimal Generalization in Trigonometric Polynomial Models 2 1