Foundations Of The Statistical Learning Theory With Samples Corrupted By Equality-expected Noise On Quasi-probability Spaces

At present, statistical learning theory based on the random sample is considered as the best theory for solving the small sample learning problems on probability spaces. But it is difficult to deal with the small samples learning problems when samples are corrupted by noise on non-probability spaces. In this paper statistical learning theory is further discussed when samples are corrupted by noise on a kind of typical non-additive measure spaces----quasi-probability spaces. The key theorem of the learning theory is given and proved when samples are corrupted by equality-expect noise on quasi-probability spaces, and the bounds on the rate of uniform convergence of the learning processes are discussed under this condition.