Hamiltonian ABC

Edward Meeds, Max Welling Robert Leenders
Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, PMLR R13:790-799, 2015.

Abstract

Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively low-dimensional problems. We introduce Hamiltonian ABC (HABC), a set of likelihood-free algorithms that apply recent advances in scaling Bayesian learning using Hamiltonian Monte Carlo (HMC) and stochastic gradients. We find that a small number forward simulations can effectively approximate the ABC gradient, allowing Hamiltonian dynamics to efficiently traverse parameter spaces. We also describe a new simple yet general approach of incorporating random seeds into the state of the Markov chain, further reducing the random walk behavior of HABC. We demonstrate HABC on several typical ABC problems, and show that HABC samples comparably to regular Bayesian inference using true gradients on a high-dimensional problem from machine learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR13-meeds15a, title = {{H}amiltonian {ABC}}, author = {Meeds, Edward and Leenders, Max Welling Robert}, booktitle = {Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence}, pages = {790--799}, year = {2015}, editor = {Meila, Marina and Heskes, Tom}, volume = {R13}, series = {Proceedings of Machine Learning Research}, month = {12--16 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r13/main/assets/meeds15a/meeds15a.pdf}, url = {https://proceedings.mlr.press/r13/meeds15a.html}, abstract = {Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively low-dimensional problems. We introduce Hamiltonian ABC (HABC), a set of likelihood-free algorithms that apply recent advances in scaling Bayesian learning using Hamiltonian Monte Carlo (HMC) and stochastic gradients. We find that a small number forward simulations can effectively approximate the ABC gradient, allowing Hamiltonian dynamics to efficiently traverse parameter spaces. We also describe a new simple yet general approach of incorporating random seeds into the state of the Markov chain, further reducing the random walk behavior of HABC. We demonstrate HABC on several typical ABC problems, and show that HABC samples comparably to regular Bayesian inference using true gradients on a high-dimensional problem from machine learning.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Hamiltonian ABC %A Edward Meeds %A Max Welling Robert Leenders %B Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2015 %E Marina Meila %E Tom Heskes %F pmlr-vR13-meeds15a %I PMLR %P 790--799 %U https://proceedings.mlr.press/r13/meeds15a.html %V R13 %X Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively low-dimensional problems. We introduce Hamiltonian ABC (HABC), a set of likelihood-free algorithms that apply recent advances in scaling Bayesian learning using Hamiltonian Monte Carlo (HMC) and stochastic gradients. We find that a small number forward simulations can effectively approximate the ABC gradient, allowing Hamiltonian dynamics to efficiently traverse parameter spaces. We also describe a new simple yet general approach of incorporating random seeds into the state of the Markov chain, further reducing the random walk behavior of HABC. We demonstrate HABC on several typical ABC problems, and show that HABC samples comparably to regular Bayesian inference using true gradients on a high-dimensional problem from machine learning. %Z Reissued by PMLR on 04 October 2026.
APA
Meeds, E. & Leenders, M.W.R.. (2015). Hamiltonian ABC. Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R13:790-799 Available from https://proceedings.mlr.press/r13/meeds15a.html. Reissued by PMLR on 04 October 2026.

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