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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.23059 |
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| _version_ | 1866918358266413056 |
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| author | Cipolla, Stefano Durastante, Fabio Gnazzo, Miryam Meini, Beatrice |
| author_facet | Cipolla, Stefano Durastante, Fabio Gnazzo, Miryam Meini, Beatrice |
| contents | Reversibility is a key property of Markov chains, central to algorithms such as Metropolis-Hastings and other MCMC methods. Yet many applications yield non-reversible chains, motivating the problem of approximating them by reversible ones with minimal modification. We formulate this task as a matrix nearness problem and focus on the practically relevant case of sparse transition matrices. The resulting optimization problem is a quadratic programming problem, and numerical experiments illustrate the effectiveness of the approach. This framework provides a principled way to enforce reversibility and sparsity patterns in Markov chains with applications in MCMC, computational chemistry, and data-driven modeling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23059 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nearest Reversible Markov Chains with Sparsity Constraints: An Optimization Approach Cipolla, Stefano Durastante, Fabio Gnazzo, Miryam Meini, Beatrice Numerical Analysis Reversibility is a key property of Markov chains, central to algorithms such as Metropolis-Hastings and other MCMC methods. Yet many applications yield non-reversible chains, motivating the problem of approximating them by reversible ones with minimal modification. We formulate this task as a matrix nearness problem and focus on the practically relevant case of sparse transition matrices. The resulting optimization problem is a quadratic programming problem, and numerical experiments illustrate the effectiveness of the approach. This framework provides a principled way to enforce reversibility and sparsity patterns in Markov chains with applications in MCMC, computational chemistry, and data-driven modeling. |
| title | Nearest Reversible Markov Chains with Sparsity Constraints: An Optimization Approach |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2602.23059 |