Optimal bounds on tail proabilities – A simplified approach

Aviad Cohen; Yuri Rabinovich; Assaf Schuster; Hadas Shachnai

doi:10.1007/3-540-64359-1_705

Optimal bounds on tail proabilities – A simplified approach

Aviad Cohen, Yuri Rabinovich, Assaf Schuster, Hadas Shachnai

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Let {X₁}^∞_i=1 be independent random variables, assuming values in [0, 1], having a common mean μ, and vaxiances bounded by σ². Let S_n∑ⁿ_i=1 X_i. We give a general and simple method for obtaining asymptotically optimal upper bounds on probabilities of events of the form {S_n - E[S_n] ≥ na} with explicit dependence on μ and σ². For general bounded random variables the method yields the Bennett inequality, with a simplified proof. For specific classes of distributions the method can be used to derive bounds that are tighter than those achieved by the Bennett inequality. We demonstrate the power of the method by applying it to the case of symmetric three-point distributions, thus improving previous results for the List Update Problem.

Original language	English
Title of host publication	Parallel and Distributed Processing - 10 IPPS/SPDP 1998 Workshops Held in Conjunction with the 12th International Parallel Processing Symposium and 9th Symposium on Parallel and Distributed Processing, Proceedings
Editors	Jose Rolim
Publisher	Springer Verlag
Pages	341-350
Number of pages	10
ISBN (Print)	3540643591, 9783540643593
DOIs	https://doi.org/10.1007/3-540-64359-1_705
State	Published - 1998
Externally published	Yes
Event	10 Workshops held in conjunction with 12th International Parallel Symposium and 9th Symposium on Parallel and Distributed Processing, IPPS/SPDP 1998 - Orlando, United States Duration: 30 Mar 1998 → 3 Apr 1998

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1388
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10 Workshops held in conjunction with 12th International Parallel Symposium and 9th Symposium on Parallel and Distributed Processing, IPPS/SPDP 1998
Country/Territory	United States
City	Orlando
Period	30/03/98 → 3/04/98

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1998.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/3-540-64359-1_705

Cite this

Cohen, A., Rabinovich, Y., Schuster, A., & Shachnai, H. (1998). Optimal bounds on tail proabilities – A simplified approach. In J. Rolim (Ed.), Parallel and Distributed Processing - 10 IPPS/SPDP 1998 Workshops Held in Conjunction with the 12th International Parallel Processing Symposium and 9th Symposium on Parallel and Distributed Processing, Proceedings (pp. 341-350). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1388). Springer Verlag. https://doi.org/10.1007/3-540-64359-1_705

Cohen, Aviad ; Rabinovich, Yuri ; Schuster, Assaf et al. / Optimal bounds on tail proabilities – A simplified approach. Parallel and Distributed Processing - 10 IPPS/SPDP 1998 Workshops Held in Conjunction with the 12th International Parallel Processing Symposium and 9th Symposium on Parallel and Distributed Processing, Proceedings. editor / Jose Rolim. Springer Verlag, 1998. pp. 341-350 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Let {X1}∞i=1 be independent random variables, assuming values in [0, 1], having a common mean μ, and vaxiances bounded by σ2. Let Sn∑ni=1 Xi. We give a general and simple method for obtaining asymptotically optimal upper bounds on probabilities of events of the form {Sn - E[Sn] ≥ na} with explicit dependence on μ and σ2. For general bounded random variables the method yields the Bennett inequality, with a simplified proof. For specific classes of distributions the method can be used to derive bounds that are tighter than those achieved by the Bennett inequality. We demonstrate the power of the method by applying it to the case of symmetric three-point distributions, thus improving previous results for the List Update Problem.",

author = "Aviad Cohen and Yuri Rabinovich and Assaf Schuster and Hadas Shachnai",

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Cohen, A, Rabinovich, Y, Schuster, A & Shachnai, H 1998, Optimal bounds on tail proabilities – A simplified approach. in J Rolim (ed.), Parallel and Distributed Processing - 10 IPPS/SPDP 1998 Workshops Held in Conjunction with the 12th International Parallel Processing Symposium and 9th Symposium on Parallel and Distributed Processing, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1388, Springer Verlag, pp. 341-350, 10 Workshops held in conjunction with 12th International Parallel Symposium and 9th Symposium on Parallel and Distributed Processing, IPPS/SPDP 1998, Orlando, United States, 30/03/98. https://doi.org/10.1007/3-540-64359-1_705

Optimal bounds on tail proabilities – A simplified approach. / Cohen, Aviad; Rabinovich, Yuri; Schuster, Assaf et al.
Parallel and Distributed Processing - 10 IPPS/SPDP 1998 Workshops Held in Conjunction with the 12th International Parallel Processing Symposium and 9th Symposium on Parallel and Distributed Processing, Proceedings. ed. / Jose Rolim. Springer Verlag, 1998. p. 341-350 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1388).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Cohen A, Rabinovich Y, Schuster A, Shachnai H. Optimal bounds on tail proabilities – A simplified approach. In Rolim J, editor, Parallel and Distributed Processing - 10 IPPS/SPDP 1998 Workshops Held in Conjunction with the 12th International Parallel Processing Symposium and 9th Symposium on Parallel and Distributed Processing, Proceedings. Springer Verlag. 1998. p. 341-350. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-64359-1_705

Optimal bounds on tail proabilities – A simplified approach

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Bibliographical note

ASJC Scopus subject areas

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