Pseudo Width In Probabilistic Setting

Width theory is closely related to computational complexity,and it becomes one of the hot topics in functional approximation theory.With the rapid development of information intelligence era,pseudo-width is more and more widely used in pattern recognition,regression estimation,empirical process,learning theory and so on.So,the study of pseudo-width has more urgent practical significance and theoretical value.This paper studies the pseudo-width in the probabilistic setting and estimates the asymptotic order of the pseudo-width of finite dimensional space and one-dimensional Sobolev space in the probabilistic setting.That is:and...