Abstract: Bounds on the rate of uniform convergence of learning process are important component part of statistical learning theory and the bounds determine the generalization abilities of learning machines.Based on the chance theory and the definition of Hybrid variable,bounds on the rate of uniform convergence of learning process based on hybrid samples are discussed and the relationship between the bounds and the capacity of the set of functions is given.

Key words: Hybrid variable, Hybrid empirical risk minimization principle, the rate of uniform convergence