The Key Theorem Of Learning Theory On Rough Random Samples

In view of the uncertainty of the real world, based on the rough random theory, the key theorem and bounds on the rate of uniform convergence of learning processes as the base of statistical learning theory were generalized in this paper. The general expression of the rough learning problem is brought forward; the rough risk function, the rough empirical risk function and rough empirical risk minimization principle are presented; the key theorem of rough random learning theory is given and proved; bounds on the rate of uniform convergence of rough learning process are discussed in the last.