Principled model selection for stochastic dynamics
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918134596763648 |
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| author | Gerardos, Andonis Ronceray, Pierre |
| author_facet | Gerardos, Andonis Ronceray, Pierre |
| contents | Complex dynamical systems, from macromolecules to ecosystems, are often modeled by stochastic differential equations. To learn such models from data, a common approach involves sparse selection among a large function library. However, we show that overfitting arises not just from individual model complexity, but also from the combinatorial growth of possible models. To address this, we introduce Parsimonious Stochastic Inference (PASTIS), a principled method combining likelihood-estimation statistics with extreme value theory to suppress superfluous parameters. PASTIS outperforms existing methods and reliably identifies minimal models, even with low sampling rates or measurement error. It extends to stochastic partial differential equations, and applies to ecological networks and reaction-diffusion dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_10339 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Principled model selection for stochastic dynamics Gerardos, Andonis Ronceray, Pierre Soft Condensed Matter Statistical Mechanics Data Analysis, Statistics and Probability Machine Learning Complex dynamical systems, from macromolecules to ecosystems, are often modeled by stochastic differential equations. To learn such models from data, a common approach involves sparse selection among a large function library. However, we show that overfitting arises not just from individual model complexity, but also from the combinatorial growth of possible models. To address this, we introduce Parsimonious Stochastic Inference (PASTIS), a principled method combining likelihood-estimation statistics with extreme value theory to suppress superfluous parameters. PASTIS outperforms existing methods and reliably identifies minimal models, even with low sampling rates or measurement error. It extends to stochastic partial differential equations, and applies to ecological networks and reaction-diffusion dynamics. |
| title | Principled model selection for stochastic dynamics |
| topic | Soft Condensed Matter Statistical Mechanics Data Analysis, Statistics and Probability Machine Learning |
| url | https://arxiv.org/abs/2501.10339 |