Generalization Bound for Innitely Divisible Empirical Process

In this paper, we study the generalization bound for an empirical process of samples in-dependently drawn from an infinitely divisi-ble (ID) distribution, which is termed as the ID empirical process. In particular, based on a martingale method, we develop devia-tion inequalities for the sequence of random variables of an ID distribution. By applying the obtained deviation inequalities, we then show the generalization bound for ID empir-ical process based on the annealed Vapnik-Chervonenkis (VC) entropy. Afterward, ac-cording to Sauer’s lemma, we get the general-ization bound for ID empirical process based on the VC dimension. Finally, by using a re-sulted result bound, we analyze the asymp-totic convergence of ID empirical process and show that the convergence rate of ID empiri-cal process can reach