Risk Bounds for Infinitely Divisible Distribution

Chao Zhang, Dacheng Tao
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:877-884, 2011.

Abstract

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).

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-zhang11a, title = {Risk Bounds for Infinitely Divisible Distribution}, author = {Zhang, Chao and Tao, Dacheng}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {877--884}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/zhang11a/zhang11a.pdf}, url = {https://proceedings.mlr.press/r9/zhang11a.html}, abstract = {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).}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Risk Bounds for Infinitely Divisible Distribution %A Chao Zhang %A Dacheng Tao %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-zhang11a %I PMLR %P 877--884 %U https://proceedings.mlr.press/r9/zhang11a.html %V R9 %X 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). %Z Reissued by PMLR on 04 October 2026.
APA
Zhang, C. & Tao, D.. (2011). Risk Bounds for Infinitely Divisible Distribution. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:877-884 Available from https://proceedings.mlr.press/r9/zhang11a.html. Reissued by PMLR on 04 October 2026.

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