Risk Bounds for Infinitely Divisible Distribution
Chao Zhang, Dacheng Tao
In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of an ID distribution with zero Gaussian component. By applying the deviation inequalities, we obtain the risk bounds based on the covering number for the ID distribution. Finally, we analyze the asymptotic convergence of the risk bound derived from one of the two deviation inequalities and show that the convergence rate of the bound is faster than the result for the generic i.i.d. empirical process (Mendelson, 2003).
PDF Link: /papers/11/p796-zhang.pdf
AUTHOR = "Chao Zhang
and Dacheng Tao",
TITLE = "Risk Bounds for Infinitely Divisible Distribution",
BOOKTITLE = "Proceedings of the Twenty-Seventh Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-11)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2011",
PAGES = "796--803"