Kernel Adaptive Metropolis-Hastings

Dino Sejdinovic, Heiko Strathmann, Maria Lomeli Garcia, Christophe Andrieu, Arthur Gretton
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):1665-1673, 2014.

Abstract

A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert space (RKHS), such that the feature space covariance of the samples informs the choice of proposal. The procedure is computationally efficient and straightforward to implement, since the RKHS moves can be integrated out analytically: our proposal distribution in the original space is a normal distribution whose mean and covariance depend on where the current sample lies in the support of the target distribution, and adapts to its local covariance structure. Furthermore, the procedure requires neither gradients nor any other higher order information about the target, making it particularly attractive for contexts such as Pseudo-Marginal MCMC. Kernel Adaptive Metropolis-Hastings outperforms competing fixed and adaptive samplers on multivariate, highly nonlinear target distributions, arising in both real-world and synthetic examples.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-sejdinovic14, title = {Kernel Adaptive Metropolis-Hastings}, author = {Sejdinovic, Dino and Strathmann, Heiko and Garcia, Maria Lomeli and Andrieu, Christophe and Gretton, Arthur}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {1665--1673}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/sejdinovic14.pdf}, url = {https://proceedings.mlr.press/v32/sejdinovic14.html}, abstract = {A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert space (RKHS), such that the feature space covariance of the samples informs the choice of proposal. The procedure is computationally efficient and straightforward to implement, since the RKHS moves can be integrated out analytically: our proposal distribution in the original space is a normal distribution whose mean and covariance depend on where the current sample lies in the support of the target distribution, and adapts to its local covariance structure. Furthermore, the procedure requires neither gradients nor any other higher order information about the target, making it particularly attractive for contexts such as Pseudo-Marginal MCMC. Kernel Adaptive Metropolis-Hastings outperforms competing fixed and adaptive samplers on multivariate, highly nonlinear target distributions, arising in both real-world and synthetic examples.} }
Endnote
%0 Conference Paper %T Kernel Adaptive Metropolis-Hastings %A Dino Sejdinovic %A Heiko Strathmann %A Maria Lomeli Garcia %A Christophe Andrieu %A Arthur Gretton %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-sejdinovic14 %I PMLR %P 1665--1673 %U https://proceedings.mlr.press/v32/sejdinovic14.html %V 32 %N 2 %X A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert space (RKHS), such that the feature space covariance of the samples informs the choice of proposal. The procedure is computationally efficient and straightforward to implement, since the RKHS moves can be integrated out analytically: our proposal distribution in the original space is a normal distribution whose mean and covariance depend on where the current sample lies in the support of the target distribution, and adapts to its local covariance structure. Furthermore, the procedure requires neither gradients nor any other higher order information about the target, making it particularly attractive for contexts such as Pseudo-Marginal MCMC. Kernel Adaptive Metropolis-Hastings outperforms competing fixed and adaptive samplers on multivariate, highly nonlinear target distributions, arising in both real-world and synthetic examples.
RIS
TY - CPAPER TI - Kernel Adaptive Metropolis-Hastings AU - Dino Sejdinovic AU - Heiko Strathmann AU - Maria Lomeli Garcia AU - Christophe Andrieu AU - Arthur Gretton BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-sejdinovic14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 1665 EP - 1673 L1 - http://proceedings.mlr.press/v32/sejdinovic14.pdf UR - https://proceedings.mlr.press/v32/sejdinovic14.html AB - A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert space (RKHS), such that the feature space covariance of the samples informs the choice of proposal. The procedure is computationally efficient and straightforward to implement, since the RKHS moves can be integrated out analytically: our proposal distribution in the original space is a normal distribution whose mean and covariance depend on where the current sample lies in the support of the target distribution, and adapts to its local covariance structure. Furthermore, the procedure requires neither gradients nor any other higher order information about the target, making it particularly attractive for contexts such as Pseudo-Marginal MCMC. Kernel Adaptive Metropolis-Hastings outperforms competing fixed and adaptive samplers on multivariate, highly nonlinear target distributions, arising in both real-world and synthetic examples. ER -
APA
Sejdinovic, D., Strathmann, H., Garcia, M.L., Andrieu, C. & Gretton, A.. (2014). Kernel Adaptive Metropolis-Hastings. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):1665-1673 Available from https://proceedings.mlr.press/v32/sejdinovic14.html.

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