The Foundation Of Statistical Learning Theory With Rough Samples

The key theorem and the bounds on the rate of convergence of learning processes provide theoretical bases for the applied research of support vector machine etc., so they play important roles in statistical learning theory. In view of the uncertainty of the real world, trust theory and statistical learning theory are combined to generalize the key theorem and the bounds on the rate of uniform convergence of learning theory. This paper mainly investigates the basic problems of statistical learning theory with rough samples. Firstly, the basic contents of trust theory are introduced; Secondly, on the basis of this theory, some concepts and theorems of trust statistics are proposed; Thirdly, Rough Empirical Risk Minimization principle is given, and the key theorem of statistical learning theory with rough samples is proved: Finally, the bounds on the rate of uniform convergence of learning processes based on Rough Empirical Risk Minimization principle are proposed.