A class of learning for optimal generalization

Learning a mapping from training data can be discussed from the viewpoint of function approximation. One of the authors, Ogawa (1995), proposed projection learning, partial projection learning, and averaged projection learning to obtain good generalization capability, and devised the concept of a family of projection learnings which includes these three kinds of projection learnings. This provided a framework to discuss an infinite kind of learning. Conventional definitions of the family, however, did not represent the concept appropriately and inhibited development of the theory. In this paper, we propose a new and natural definition and discuss properties of the family, which provide the foundations of future studies of the family of projection learnings.