Learning bounds for a generalized family of Bayesian posterior distributions

Tong Zhang

Learning bounds for a generalized family of Bayesian posterior distributions

Tong Zhang

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

Abstract

In this paper we obtain convergence bounds for the concentration of Bayesian posterior distributions (around the true distribution) using a novel method that simplifies and enhances previous results. Based on the analysis, we also introduce a generalized family of Bayesian posteriors, and show that the convergence behavior of these generalized posteriors is completely determined by the local prior structure around the true distribution. This important and surprising robustness property does not hold for the standard Bayesian posterior in that it may not concentrate when there exist "bad" prior structures even at places far away from the true distribution.

Original language	English (US)
Title of host publication	Advances in Neural Information Processing Systems 16 - Proceedings of the 2003 Conference, NIPS 2003
Publisher	Neural information processing systems foundation
ISBN (Print)	0262201526, 9780262201520
State	Published - 2004
Externally published	Yes
Event	17th Annual Conference on Neural Information Processing Systems, NIPS 2003 - Vancouver, BC, Canada Duration: Dec 8 2003 → Dec 13 2003

Publication series

Name	Advances in Neural Information Processing Systems
ISSN (Print)	1049-5258

Other

Other	17th Annual Conference on Neural Information Processing Systems, NIPS 2003
Country/Territory	Canada
City	Vancouver, BC
Period	12/8/03 → 12/13/03

ASJC Scopus subject areas

Computer Networks and Communications
Information Systems
Signal Processing

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Learning bounds for a generalized family of Bayesian posterior distributions. / Zhang, Tong.
Advances in Neural Information Processing Systems 16 - Proceedings of the 2003 Conference, NIPS 2003. Neural information processing systems foundation, 2004. (Advances in Neural Information Processing Systems).

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

Zhang, T 2004, Learning bounds for a generalized family of Bayesian posterior distributions. in Advances in Neural Information Processing Systems 16 - Proceedings of the 2003 Conference, NIPS 2003. Advances in Neural Information Processing Systems, Neural information processing systems foundation, 17th Annual Conference on Neural Information Processing Systems, NIPS 2003, Vancouver, BC, Canada, 12/8/03.

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AB - In this paper we obtain convergence bounds for the concentration of Bayesian posterior distributions (around the true distribution) using a novel method that simplifies and enhances previous results. Based on the analysis, we also introduce a generalized family of Bayesian posteriors, and show that the convergence behavior of these generalized posteriors is completely determined by the local prior structure around the true distribution. This important and surprising robustness property does not hold for the standard Bayesian posterior in that it may not concentrate when there exist "bad" prior structures even at places far away from the true distribution.

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ER -

Learning bounds for a generalized family of Bayesian posterior distributions

Abstract

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Other

ASJC Scopus subject areas

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