Efficient MCMC sampling with dimension-free convergence rate using ADMM-type splitting
Performing exact Bayesian inference for complex models is computationally intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are expensive for large data sets and high-dimensional models. A standard approach to mitigate this...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Journal of Machine Learning Research
2022
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| _version_ | 1826278267910356992 |
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| author | Vono, M Paulin, D Doucet, A |
| author_facet | Vono, M Paulin, D Doucet, A |
| author_sort | Vono, M |
| collection | OXFORD |
| description | Performing exact Bayesian inference for complex models is computationally intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are expensive for large data sets and high-dimensional models. A standard approach to mitigate this complexity consists in using subsampling techniques or distributing the data across a cluster. However, these approaches are typically unreliable in high-dimensional scenarios. We focus here on a recent alternative class of MCMC schemes exploiting a splitting strategy akin to the one used by the celebrated alternating direction method of multipliers (ADMM) optimization algorithm. These methods appear to provide empirically state-of-the-art performance but their theoretical behavior in high dimension is currently unknown. In this paper, we propose a detailed theoretical study of one of these algorithms known as the split Gibbs sampler. Under regularity conditions, we establish explicit convergence rates for this scheme using Ricci curvature and coupling ideas. We support our theory with numerical illustrations. |
| first_indexed | 2024-03-06T23:41:24Z |
| format | Journal article |
| id | oxford-uuid:6f71323d-393b-4a27-87b5-4f4b8cff6ba0 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:41:24Z |
| publishDate | 2022 |
| publisher | Journal of Machine Learning Research |
| record_format | dspace |
| spelling | oxford-uuid:6f71323d-393b-4a27-87b5-4f4b8cff6ba02022-03-26T19:30:43ZEfficient MCMC sampling with dimension-free convergence rate using ADMM-type splittingJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6f71323d-393b-4a27-87b5-4f4b8cff6ba0EnglishSymplectic ElementsJournal of Machine Learning Research2022Vono, MPaulin, DDoucet, APerforming exact Bayesian inference for complex models is computationally intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are expensive for large data sets and high-dimensional models. A standard approach to mitigate this complexity consists in using subsampling techniques or distributing the data across a cluster. However, these approaches are typically unreliable in high-dimensional scenarios. We focus here on a recent alternative class of MCMC schemes exploiting a splitting strategy akin to the one used by the celebrated alternating direction method of multipliers (ADMM) optimization algorithm. These methods appear to provide empirically state-of-the-art performance but their theoretical behavior in high dimension is currently unknown. In this paper, we propose a detailed theoretical study of one of these algorithms known as the split Gibbs sampler. Under regularity conditions, we establish explicit convergence rates for this scheme using Ricci curvature and coupling ideas. We support our theory with numerical illustrations. |
| spellingShingle | Vono, M Paulin, D Doucet, A Efficient MCMC sampling with dimension-free convergence rate using ADMM-type splitting |
| title | Efficient MCMC sampling with dimension-free convergence rate using ADMM-type splitting |
| title_full | Efficient MCMC sampling with dimension-free convergence rate using ADMM-type splitting |
| title_fullStr | Efficient MCMC sampling with dimension-free convergence rate using ADMM-type splitting |
| title_full_unstemmed | Efficient MCMC sampling with dimension-free convergence rate using ADMM-type splitting |
| title_short | Efficient MCMC sampling with dimension-free convergence rate using ADMM-type splitting |
| title_sort | efficient mcmc sampling with dimension free convergence rate using admm type splitting |
| work_keys_str_mv | AT vonom efficientmcmcsamplingwithdimensionfreeconvergencerateusingadmmtypesplitting AT paulind efficientmcmcsamplingwithdimensionfreeconvergencerateusingadmmtypesplitting AT douceta efficientmcmcsamplingwithdimensionfreeconvergencerateusingadmmtypesplitting |