Improving the asymptotic performance of Markov chain Monte-Carlo by inserting vortices

Yi Sun; Faustino Gomez; Jürgen Schmidhuber

Improving the asymptotic performance of Markov chain Monte-Carlo by inserting vortices

Yi Sun, Faustino Gomez, Jürgen Schmidhuber

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

Abstract

We present a new way of converting a reversible finite Markov chain into a nonreversible one, with a theoretical guarantee that the asymptotic variance of the MCMC estimator based on the non-reversible chain is reduced. The method is applicable to any reversible chain whose states are not connected through a tree, and can be interpreted graphically as inserting vortices into the state transition graph. Our result confirms that non-reversible chains are fundamentally better than reversible ones in terms of asymptotic performance, and suggests interesting directions for further improving MCMC.

Original language	English (US)
Title of host publication	Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010
State	Published - Dec 1 2010
Externally published	Yes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2022-09-14

Cite this

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title = "Improving the asymptotic performance of Markov chain Monte-Carlo by inserting vortices",

abstract = "We present a new way of converting a reversible finite Markov chain into a nonreversible one, with a theoretical guarantee that the asymptotic variance of the MCMC estimator based on the non-reversible chain is reduced. The method is applicable to any reversible chain whose states are not connected through a tree, and can be interpreted graphically as inserting vortices into the state transition graph. Our result confirms that non-reversible chains are fundamentally better than reversible ones in terms of asymptotic performance, and suggests interesting directions for further improving MCMC.",

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year = "2010",

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isbn = "9781617823800",

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AU - Sun, Yi

AU - Gomez, Faustino

AU - Schmidhuber, Jürgen

N1 - Generated from Scopus record by KAUST IRTS on 2022-09-14

PY - 2010/12/1

Y1 - 2010/12/1

N2 - We present a new way of converting a reversible finite Markov chain into a nonreversible one, with a theoretical guarantee that the asymptotic variance of the MCMC estimator based on the non-reversible chain is reduced. The method is applicable to any reversible chain whose states are not connected through a tree, and can be interpreted graphically as inserting vortices into the state transition graph. Our result confirms that non-reversible chains are fundamentally better than reversible ones in terms of asymptotic performance, and suggests interesting directions for further improving MCMC.

AB - We present a new way of converting a reversible finite Markov chain into a nonreversible one, with a theoretical guarantee that the asymptotic variance of the MCMC estimator based on the non-reversible chain is reduced. The method is applicable to any reversible chain whose states are not connected through a tree, and can be interpreted graphically as inserting vortices into the state transition graph. Our result confirms that non-reversible chains are fundamentally better than reversible ones in terms of asymptotic performance, and suggests interesting directions for further improving MCMC.

UR - http://www.scopus.com/inward/record.url?scp=84860631900&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781617823800

BT - Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010

ER -

Improving the asymptotic performance of Markov chain Monte-Carlo by inserting vortices

Abstract

Bibliographical note

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