Optimal Scaling Results for Moreau-Yosida Metropolis-adjusted Langevin Algorithms
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911925307179008 |
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| author | Crucinio, Francesca R. Durmus, Alain Jiménez, Pablo Roberts, Gareth O. |
| author_facet | Crucinio, Francesca R. Durmus, Alain Jiménez, Pablo Roberts, Gareth O. |
| contents | We consider a recently proposed class of MCMC methods which uses proximity maps instead of gradients to build proposal mechanisms which can be employed for both differentiable and non-differentiable targets. These methods have been shown to be stable for a wide class of targets, making them a valuable alternative to Metropolis-adjusted Langevin algorithms (MALA); and have found wide application in imaging contexts. The wider stability properties are obtained by building the Moreau-Yosida envelope for the target of interest, which depends on a parameter $λ$. In this work, we investigate the optimal scaling problem for this class of algorithms, which encompasses MALA, and provide practical guidelines for the implementation of these methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2301_02446 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal Scaling Results for Moreau-Yosida Metropolis-adjusted Langevin Algorithms Crucinio, Francesca R. Durmus, Alain Jiménez, Pablo Roberts, Gareth O. Computation Probability Statistics Theory 65C05, 60F05 We consider a recently proposed class of MCMC methods which uses proximity maps instead of gradients to build proposal mechanisms which can be employed for both differentiable and non-differentiable targets. These methods have been shown to be stable for a wide class of targets, making them a valuable alternative to Metropolis-adjusted Langevin algorithms (MALA); and have found wide application in imaging contexts. The wider stability properties are obtained by building the Moreau-Yosida envelope for the target of interest, which depends on a parameter $λ$. In this work, we investigate the optimal scaling problem for this class of algorithms, which encompasses MALA, and provide practical guidelines for the implementation of these methods. |
| title | Optimal Scaling Results for Moreau-Yosida Metropolis-adjusted Langevin Algorithms |
| topic | Computation Probability Statistics Theory 65C05, 60F05 |
| url | https://arxiv.org/abs/2301.02446 |