Some Theoretical Studies on Learning Theory with Samples Corrupted by Noise

In statistical learning theory (SLT), the key theorem and the bounds on the rate of uniform convergence of learning processes provide theoretical basis for the applied research of support vector machine etc., so they play important roles in SLT. In the study of two aspects, samples which we deal with are supposed to be noise-free. But it is not always the case because of the influence of human or environmental factors. With a view of this, we propose and prove the key theorem and discuss the bounds on the rate of uniform convergence of learning processes when samples are corrupted by noise