Kernel Adaptive Metropolis-Hastings

Dino Sejdinovic, Heiko Strathmann, Maria Lomeli Garcia, Christophe Andrieu, Arthur Gretton

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

7 Citations (Scopus)

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.

Original languageEnglish
Title of host publication31st International Conference on Machine Learning, ICML 2014
PublisherInternational Machine Learning Society (IMLS)
Pages3640-3653
Number of pages14
Volume5
ISBN (Print)9781634393973
Publication statusPublished - 2014
Event31st International Conference on Machine Learning, ICML 2014 - Beijing, China
Duration: 21 Jun 201426 Jun 2014

Conference

Conference31st International Conference on Machine Learning, ICML 2014
CountryChina
CityBeijing
Period21/06/1426/06/14

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  • Cite this

    Sejdinovic, D., Strathmann, H., Garcia, M. L., Andrieu, C., & Gretton, A. (2014). Kernel Adaptive Metropolis-Hastings. In 31st International Conference on Machine Learning, ICML 2014 (Vol. 5, pp. 3640-3653). International Machine Learning Society (IMLS).