Bounds on the rate of uniform convergence of learning processes about samples corrupted by noise on credibility space

Abstract

The bounds on the rate of convergence of learning processes play an important role in statistical learning theory. However, the researches about them presently only focus on probability measure (additive measure) space. And the samples we deal with are supposed to be noise-free. This paper explores the statistical learning theory on credibility space. The theory of consistency of the empirical risk minimization principle when samples are corrupted by noise is established on credibility space; the bounds on the rate of uniform convergence of learning processes about samples corrupted by noise is proposed and proven on the non-additive measure space.