Active learning for optimal generalization in trigonometric polynomial models

In this paper, we consider the problem of active learning, and give a neces sary and sufficient condition of sample points for the optimal generalizati on capability. By utilizing the properties of pseudo orthogonal bases, we c larify the mechanism of achieving the optimal generalization capability. We also show that the condition does not only provide the optimal generalizat ion capability but also reduces the computational complexity and memory req uired to calculate learning result functions. Based on the optimality condi tion, we give design methods of optimal sample points for trigonometric pol ynomial models. Finally, the effectiveness of the proposed active learning method is demonstrated through computer simulations.