Accelerated Markov Chain Monte Carlo Using Adaptive Weighting Scheme Article Swipe
Yan‐Bo Wang
,
Wenyu Chen
,
Shimin Shan
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2408.12888
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2408.12888
Gibbs sampling is one of the most commonly used Markov Chain Monte Carlo (MCMC) algorithms due to its simplicity and efficiency. It cycles through the latent variables, sampling each one from its distribution conditional on the current values of all the other variables. Conventional Gibbs sampling is based on the systematic scan (with a deterministic order of variables). In contrast, in recent years, Gibbs sampling with random scan has shown its advantage in some scenarios. However, almost all the analyses of Gibbs sampling with the random scan are based on uniform selection of variables. In this paper, we focus on a random scan Gibbs sampling method that selects each latent variable non-uniformly. Firstly, we show that this non-uniform scan Gibbs sampling leaves the target posterior distribution invariant. Then we explore how to determine the selection probability for latent variables. In particular, we construct an objective as a function of the selection probability and solve the constrained optimization problem. We further derive an analytic solution of the selection probability, which can be estimated easily. Our algorithm relies on the simple intuition that choosing the variable updates according to their marginal probabilities enhances the mixing time of the Markov chain. Finally, we validate the effectiveness of the proposed Gibbs sampler by conducting a set of experiments on real-world applications.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2408.12888
- https://arxiv.org/pdf/2408.12888
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4402699085
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https://openalex.org/W4402699085Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2408.12888Digital Object Identifier
- Title
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Accelerated Markov Chain Monte Carlo Using Adaptive Weighting SchemeWork title
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-08-23Full publication date if available
- Authors
-
Yan‐Bo Wang, Wenyu Chen, Shimin ShanList of authors in order
- Landing page
-
https://arxiv.org/abs/2408.12888Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2408.12888Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2408.12888Direct OA link when available
- Concepts
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Markov chain Monte Carlo, Weighting, Scheme (mathematics), Markov chain, Monte Carlo method, Computer science, Statistical physics, Algorithm, Mathematics, Mathematical optimization, Statistics, Machine learning, Physics, Mathematical analysis, AcousticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile |