:ge,hf2=$n$?$a$ng=f03x=, Active Learning for Optimal Generalization

In this paper, we consider the problem of active learning in trigonometric polynomial networks and give a necessary and sufficient 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, we give examples of sample points satisfying the condition and show that one of the examples further reduces the computational complexity and memory required for the calculation.