ML Anthology

Risk Bounds for Infinitely Divisible Distribution

Chao Zhang, Dacheng Tao
UAI 2011 pp. 796-803
/uai/2011/zhang2011uai-risk/

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).

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Cite

Text

Zhang and Tao. "Risk Bounds for Infinitely Divisible Distribution." Conference on Uncertainty in Artificial Intelligence, 2011.

Markdown

[Zhang and Tao. "Risk Bounds for Infinitely Divisible Distribution." Conference on Uncertainty in Artificial Intelligence, 2011.](https://mlanthology.org/uai/2011/zhang2011uai-risk/)

BibTeX

@inproceedings{zhang2011uai-risk,
  title     = {{Risk Bounds for Infinitely Divisible Distribution}},
  author    = {Zhang, Chao and Tao, Dacheng},
  booktitle = {Conference on Uncertainty in Artificial Intelligence},
  year      = {2011},
  pages     = {796-803},
  url       = {https://mlanthology.org/uai/2011/zhang2011uai-risk/}
}