Basic Research of Statistical Learning with Trust Theory Based Rough Sample

The key theorem of statistical learning theory provides a theoretical basis for the research of Support Vector Machines, and the bounds on the rate of uniform convergence of learning theory describe the generalization ability of learning machine. In contrast to probabilistic sample in the classical statistical learning theory, trust theory based rough sample is considered in the paper. The key theorem of learning theory with rough sample is proposed and proved, and the bounds on the rate of uniform convergence of learning process with rough sample are given and proved. They may provide some theoretical bases useful in additional applications of learning theory and Support Vector Machines.