The Bound for the Rate of Uniform Convergence for Learning Machine Based on \alpha-mixing Sequence

It has been shown previously by Vapnik, Cucker and Smale that, the empirical risks based on an independent and identically distributed (i.i.d.) sequence must uniformly converge to their expected risks for learning machines as the number of samples approaches infinity. This paper extends the results to the case where the i.i.d. sequence replaced by \alpha-mixing sequence. It establishes the rate of uniform convergence for learning machine based on \alpha-mixing sequence by applying Markov's inequality.