We obtain the tail probability of generalized sub-Gaussian canonical
processes. It can be viewed as a variant of the Bernstein-type inequality in
the i.i.d case, and we further get a tighter bound of concentration inequality
through uniformly randomized techniques. A concentration inequality for general
functions involving independent random variables is also derived as an
extension. As for applications, we derive convergence results for principal
component analysis and the Rademacher complexities method.Comment: 25page