Shadow Manifold Hamiltonian Monte Carlo

Chris van der Heide, Fred Roosta, Liam Hodgkinson, Dirk Kroese
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1477-1485, 2021.

Abstract

Hamiltonian Monte Carlo and its descendants have found success in machine learning and computational statistics due to their ability to draw samples in high dimensions with greater efficiency than classical MCMC. One of these derivatives, Riemannian manifold Hamiltonian Monte Carlo (RMHMC), better adapts the sampler to the geometry of the target density, allowing for improved performances in sampling problems with complex geometric features. Other approaches have boosted acceptance rates by sampling from an integrator-dependent “shadow density” and compensating for the induced bias via importance sampling. We combine the benefits of RMHMC with those attained by sampling from the shadow density, by deriving the shadow Hamiltonian corresponding to the generalized leapfrog integrator used in RMHMC. This leads to a new algorithm, shadow manifold Hamiltonian Monte Carlo, that shows improved performance over RMHMC, and leaves the target density invariant.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-heide21a, title = { Shadow Manifold Hamiltonian Monte Carlo }, author = {van der Heide, Chris and Roosta, Fred and Hodgkinson, Liam and Kroese, Dirk}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {1477--1485}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/heide21a/heide21a.pdf}, url = {https://proceedings.mlr.press/v130/heide21a.html}, abstract = { Hamiltonian Monte Carlo and its descendants have found success in machine learning and computational statistics due to their ability to draw samples in high dimensions with greater efficiency than classical MCMC. One of these derivatives, Riemannian manifold Hamiltonian Monte Carlo (RMHMC), better adapts the sampler to the geometry of the target density, allowing for improved performances in sampling problems with complex geometric features. Other approaches have boosted acceptance rates by sampling from an integrator-dependent “shadow density” and compensating for the induced bias via importance sampling. We combine the benefits of RMHMC with those attained by sampling from the shadow density, by deriving the shadow Hamiltonian corresponding to the generalized leapfrog integrator used in RMHMC. This leads to a new algorithm, shadow manifold Hamiltonian Monte Carlo, that shows improved performance over RMHMC, and leaves the target density invariant. } }
Endnote
%0 Conference Paper %T Shadow Manifold Hamiltonian Monte Carlo %A Chris van der Heide %A Fred Roosta %A Liam Hodgkinson %A Dirk Kroese %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-heide21a %I PMLR %P 1477--1485 %U https://proceedings.mlr.press/v130/heide21a.html %V 130 %X Hamiltonian Monte Carlo and its descendants have found success in machine learning and computational statistics due to their ability to draw samples in high dimensions with greater efficiency than classical MCMC. One of these derivatives, Riemannian manifold Hamiltonian Monte Carlo (RMHMC), better adapts the sampler to the geometry of the target density, allowing for improved performances in sampling problems with complex geometric features. Other approaches have boosted acceptance rates by sampling from an integrator-dependent “shadow density” and compensating for the induced bias via importance sampling. We combine the benefits of RMHMC with those attained by sampling from the shadow density, by deriving the shadow Hamiltonian corresponding to the generalized leapfrog integrator used in RMHMC. This leads to a new algorithm, shadow manifold Hamiltonian Monte Carlo, that shows improved performance over RMHMC, and leaves the target density invariant.
APA
van der Heide, C., Roosta, F., Hodgkinson, L. & Kroese, D.. (2021). Shadow Manifold Hamiltonian Monte Carlo . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1477-1485 Available from https://proceedings.mlr.press/v130/heide21a.html.

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