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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.06251 |
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| _version_ | 1866917792828096512 |
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| author | Li, Guanxun Smith, Aaron Zhou, Quan |
| author_facet | Li, Guanxun Smith, Aaron Zhou, Quan |
| contents | We show that for any multiple-try Metropolis algorithm, one can always accept the proposal and evaluate the importance weight that is needed to correct for the bias without extra computational cost. This results in a general, convenient, and rejection-free Markov chain Monte Carlo (MCMC) sampling scheme. By further leveraging the importance sampling perspective on Metropolis--Hastings algorithms, we propose an alternative MCMC sampler on discrete spaces that is also outside the Metropolis--Hastings framework, along with a general theory on its complexity. Numerical examples suggest that the proposed algorithms are consistently more efficient than the original Metropolis--Hastings versions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06251 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Importance is Important: Generalized Markov Chain Importance Sampling Methods Li, Guanxun Smith, Aaron Zhou, Quan Computation Methodology Machine Learning 65C05, 60J10 We show that for any multiple-try Metropolis algorithm, one can always accept the proposal and evaluate the importance weight that is needed to correct for the bias without extra computational cost. This results in a general, convenient, and rejection-free Markov chain Monte Carlo (MCMC) sampling scheme. By further leveraging the importance sampling perspective on Metropolis--Hastings algorithms, we propose an alternative MCMC sampler on discrete spaces that is also outside the Metropolis--Hastings framework, along with a general theory on its complexity. Numerical examples suggest that the proposed algorithms are consistently more efficient than the original Metropolis--Hastings versions. |
| title | Importance is Important: Generalized Markov Chain Importance Sampling Methods |
| topic | Computation Methodology Machine Learning 65C05, 60J10 |
| url | https://arxiv.org/abs/2304.06251 |