Risk Bounds for Levy Processes in the PACLearning Framework

13th International Conference on Artificial Intelligence and Statistics

计算机科学;数学科学

Chao Zhang Dacheng Tao

PID  :  119714

来源: CEUR

【 摘 要 】

Levy processes play an important role in the stochastic process theory. However, since samples are noni.i.d., statistical learning re sults based on the i.i.d. scenarios cannot be utilized to study the risk bounds for Levy processes. In this paper, we present risk bounds for noni.i.d. samples drawn from Levy processes in the PAClearning frame work. In particular, by using a concentra tion inequality for infinitely divisible distri butions, we first prove that the function of risk error is Lipschitz continuous with a high probability, and then by using a specific con centration inequality for Levy processes, we obtain the risk bounds for noni.i.d. samples drawn from Levy processes without Gaus sian components. Based on the resulted risk bounds, we analyze the factors that affect the convergence of the risk bounds and then