Implicit langevin algorithms for sampling from log-concave densities
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108428253. Available under License Creative Commons Attribution 4.0. |
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Description
For sampling from a log-concave density, we study implicit integrators resulting from θ- method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the resulting sampling methods for θ ∈ [0; 1] and a range of step sizes are established. Our results generalize and extend prior works in several directions. In particular, for θ ≥ 1/2, we prove geometric ergodicity and stability of the resulting methods for all step sizes. We show that obtaining subsequent samples amounts to solving a strongly-convex optimization problem, which is readily achievable using one of numerous existing methods. Numerical examples supporting our theoretical analysis are also presented.
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| ID Code: | 229855 |
|---|---|
| Item Type: | Contribution to Journal (Journal Article) |
| Refereed: | Yes |
| Additional Information: | Funding Information: All authors have been supported by the Australian Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) under grant number CE140100049. Liam Hodgkinson acknowledges the support of an Australian Research Training Program (RTP) Scholarship. Fred Roosta was partially supported by the Australian Research Council through a Discovery Early Career Researcher Award (DE180100923). Part of this work was done while Fred Roosta was visiting the Simons Institute for the Theory of Computing. |
| Measurements or Duration: | 30 pages |
| Keywords: | Bayesian regression, Implicit integrators, MCMC, Sampling |
| ISSN: | 1532-4435 |
| Pure ID: | 108428253 |
| Divisions: | Current > Research Centres > Centre for Data Science Current > QUT Faculties and Divisions > Faculty of Science Current > Schools > School of Mathematical Sciences |
| Funding Information: | All authors have been supported by the Australian Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) under grant number CE140100049. Liam Hodgkinson acknowledges the support of an Australian Research Training Program (RTP) Scholarship. Fred Roosta was partially supported by the Australian Research Council through a Discovery Early Career Researcher Award (DE180100923). Part of this work was done while Fred Roosta was visiting the Simons Institute for the Theory of Computing. |
| Funding: | |
| Copyright Owner: | 2021 The Author(s) |
| Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au |
| Deposited On: | 19 Apr 2022 03:24 |
| Last Modified: | 07 May 2024 23:45 |
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