Probabilistic cellular automata with local transition matrices: synchronization, ergodicity, and inference
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909620127137792 |
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| author | Bayraktar, Erhan Lu, Fei Maggioni, Mauro Wu, Ruoyu Yang, Sichen |
| author_facet | Bayraktar, Erhan Lu, Fei Maggioni, Mauro Wu, Ruoyu Yang, Sichen |
| contents | We introduce a new class of probabilistic cellular automata that are capable of exhibiting rich dynamics such as synchronization and ergodicity and can be easily inferred from data. The system is a finite-state locally interacting Markov chain on a circular graph. Each site's subsequent state is random, with a distribution determined by its neighborhood's empirical distribution multiplied by a local transition matrix. We establish sufficient and necessary conditions on the local transition matrix for synchronization and ergodicity. Also, we introduce novel least squares estimators for inferring the local transition matrix from various types of data, which may consist of either multiple trajectories, a long trajectory, or ensemble sequences without trajectory information. Under suitable identifiability conditions, we show the asymptotic normality of these estimators and provide non-asymptotic bounds for their accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02928 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probabilistic cellular automata with local transition matrices: synchronization, ergodicity, and inference Bayraktar, Erhan Lu, Fei Maggioni, Mauro Wu, Ruoyu Yang, Sichen Probability Statistics Theory 60J10, 62F12 We introduce a new class of probabilistic cellular automata that are capable of exhibiting rich dynamics such as synchronization and ergodicity and can be easily inferred from data. The system is a finite-state locally interacting Markov chain on a circular graph. Each site's subsequent state is random, with a distribution determined by its neighborhood's empirical distribution multiplied by a local transition matrix. We establish sufficient and necessary conditions on the local transition matrix for synchronization and ergodicity. Also, we introduce novel least squares estimators for inferring the local transition matrix from various types of data, which may consist of either multiple trajectories, a long trajectory, or ensemble sequences without trajectory information. Under suitable identifiability conditions, we show the asymptotic normality of these estimators and provide non-asymptotic bounds for their accuracy. |
| title | Probabilistic cellular automata with local transition matrices: synchronization, ergodicity, and inference |
| topic | Probability Statistics Theory 60J10, 62F12 |
| url | https://arxiv.org/abs/2405.02928 |