Lagrangian Manifold Monte Carlo on Monge Patches
View / Open Files
Publication Date
2022Journal Title
INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 151
Conference Name
International Conference on Artificial Intelligence and Statistics (AISTATS '22)
ISSN
2640-3498
Publisher
PMLR
Type
Article
This Version
AM
Metadata
Show full item recordCitation
Hartmann, M., Girolami, M., & Klami, A. (2022). Lagrangian Manifold Monte Carlo on Monge Patches. INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 151 https://doi.org/10.17863/CAM.81980
Abstract
The efficiency of Markov Chain Monte Carlo (MCMC) depends on how the
underlying geometry of the problem is taken into account. For distributions
with strongly varying curvature, Riemannian metrics help in efficient
exploration of the target distribution. Unfortunately, they have significant
computational overhead due to e.g. repeated inversion of the metric tensor, and
current geometric MCMC methods using the Fisher information matrix to induce
the manifold are in practice slow. We propose a new alternative Riemannian
metric for MCMC, by embedding the target distribution into a higher-dimensional
Euclidean space as a Monge patch and using the induced metric determined by
direct geometric reasoning. Our metric only requires first-order gradient
information and has fast inverse and determinants, and allows reducing the
computational complexity of individual iterations from cubic to quadratic in
the problem dimensionality. We demonstrate how Lagrangian Monte Carlo in this
metric efficiently explores the target distributions.
Keywords
stat.ME, stat.ME, cs.AI, cs.LG
Sponsorship
Engineering and Physical Sciences Research Council (EP/R034710/1)
Royal Academy of Engineering (RAEng) (RCSRF\1718\6\34)
EPSRC (via University of Warwick) (EP/R034710/1)
EPSRC (EP/V056441/1)
Engineering and Physical Sciences Research Council (EP/V056522/1)
Embargo Lift Date
2100-01-01
Identifiers
This record's DOI: https://doi.org/10.17863/CAM.81980
This record's URL: https://www.repository.cam.ac.uk/handle/1810/334561
Statistics
Total file downloads (since January 2020). For more information on metrics see the
IRUS guide.
Recommended or similar items
The current recommendation prototype on the Apollo Repository will be turned off on 03 February 2023. Although the pilot has been fruitful for both parties, the service provider IKVA is focusing on horizon scanning products and so the recommender service can no longer be supported. We recognise the importance of recommender services in supporting research discovery and are evaluating offerings from other service providers. If you would like to offer feedback on this decision please contact us on: support@repository.cam.ac.uk