Identifying Markov chain models from time-to-event data: an algebraic approach
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915022527004672 |
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| author | Radulescu, Ovidiu Grigoriev, Dima Seiss, Matthias Douaihy, Maria Lagha, Mounia Bertrand, Edouard |
| author_facet | Radulescu, Ovidiu Grigoriev, Dima Seiss, Matthias Douaihy, Maria Lagha, Mounia Bertrand, Edouard |
| contents | Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. We solve the inverse problem: given a phase-type distribution, can we identify the transition rate parameters of the underlying Markov chain? For a specific class of solvable Markov models, we show this problem has a unique solution up to finite symmetry transformations, and we outline a recursive method for computing symbolic solutions for these models across any number of states. Using the Thomas decomposition technique from computer algebra, we further provide symbolic solutions for any model. Interestingly, different models with the same state count but distinct transition graphs can yield identical phase-type distributions. To distinguish among these, we propose additional properties beyond just the time to the next event. We demonstrate the method's applicability by inferring transcriptional regulation models from single-cell transcription imaging data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03593 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Identifying Markov chain models from time-to-event data: an algebraic approach Radulescu, Ovidiu Grigoriev, Dima Seiss, Matthias Douaihy, Maria Lagha, Mounia Bertrand, Edouard Dynamical Systems Quantitative Methods 60J28 Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. We solve the inverse problem: given a phase-type distribution, can we identify the transition rate parameters of the underlying Markov chain? For a specific class of solvable Markov models, we show this problem has a unique solution up to finite symmetry transformations, and we outline a recursive method for computing symbolic solutions for these models across any number of states. Using the Thomas decomposition technique from computer algebra, we further provide symbolic solutions for any model. Interestingly, different models with the same state count but distinct transition graphs can yield identical phase-type distributions. To distinguish among these, we propose additional properties beyond just the time to the next event. We demonstrate the method's applicability by inferring transcriptional regulation models from single-cell transcription imaging data. |
| title | Identifying Markov chain models from time-to-event data: an algebraic approach |
| topic | Dynamical Systems Quantitative Methods 60J28 |
| url | https://arxiv.org/abs/2311.03593 |