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Geometrical Recombination Operators for Real-Coded Evolutionary MCMCs

Geometrical Recombination Operators for Real-Coded Evolutionary MCMCs Markov chain Monte Carlo (MCMC) algorithms are sampling methods for intractable distributions. In this paper, we propose and investigate algorithms that improve the sampling process from multi-dimensional real-coded spaces. We present MCMC algorithms that run a population of samples and apply recombination operators in order to exchange useful information and preserve commonalities in highly probable individual states. We call this class of algorithms Evolutionary MCMCs (EMCMCs). We introduce and analyze various recombination operators which generate new samples by use of linear transformations, for instance, by translation or rotation. These recombination methods discover specific structures in the search space and adapt the population samples to the proposal distribution. We investigate how to integrate recombination in the MCMC framework to sample from a desired distribution. The recombination operators generate individuals with a computational effort that scales linearly in the number of dimensions and the number of parents. We present results from experiments conducted on a mixture of multivariate normal distributions. These results show that the recombinative EMCMCs outperform the standard MCMCs for target distributions that have a nontrivial structural relationship between the dimensions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Evolutionary Computation MIT Press

Geometrical Recombination Operators for Real-Coded Evolutionary MCMCs

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References (26)

Publisher
MIT Press
Copyright
© 2010 by the Massachusetts Institute of Technology
ISSN
1063-6560
eISSN
1530-9304
DOI
10.1162/evco.2010.18.2.18201
pmid
20210599
Publisher site
See Article on Publisher Site

Abstract

Markov chain Monte Carlo (MCMC) algorithms are sampling methods for intractable distributions. In this paper, we propose and investigate algorithms that improve the sampling process from multi-dimensional real-coded spaces. We present MCMC algorithms that run a population of samples and apply recombination operators in order to exchange useful information and preserve commonalities in highly probable individual states. We call this class of algorithms Evolutionary MCMCs (EMCMCs). We introduce and analyze various recombination operators which generate new samples by use of linear transformations, for instance, by translation or rotation. These recombination methods discover specific structures in the search space and adapt the population samples to the proposal distribution. We investigate how to integrate recombination in the MCMC framework to sample from a desired distribution. The recombination operators generate individuals with a computational effort that scales linearly in the number of dimensions and the number of parents. We present results from experiments conducted on a mixture of multivariate normal distributions. These results show that the recombinative EMCMCs outperform the standard MCMCs for target distributions that have a nontrivial structural relationship between the dimensions.

Journal

Evolutionary ComputationMIT Press

Published: Jun 1, 2010

Keywords: Markov chain Monte Carlo; sampling; evolutionary Markov chain Monte Carlo; simplex recombinations; linear transformations; real-coded search spaces

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