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Poster

Improving the Asymptotic Performance of Markov Chain Monte-Carlo by Inserting Vortices

Yi Sun · Faustino Gomez · Jürgen Schmidhuber


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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