Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912955317092352 |
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| author | van Seeventer, Gijs Salehkaleybar, Saber |
| author_facet | van Seeventer, Gijs Salehkaleybar, Saber |
| contents | We study identifiability in continuous-time linear stationary stochastic differential equations with known causal structure. Unlike existing approaches, we relax the assumption of a known diffusion matrix, thereby respecting the model's intrinsic scale invariance. Rather than recovering drift coefficients themselves, we introduce edge-sign identifiability: for a given causal structure, we ask whether the sign of a given drift entry is uniquely determined across all observational covariance matrices induced by parametrizations compatible with that structure. Under a notion of faithfulness, we derive criteria for characterising identifiability, non-identifiability, and partial identifiability for general graphs. Applying our criteria to specific causal structures, both analogous to classical causal settings (e.g., instrumental variables) and novel cyclic settings, we determine their edge-sign identifiability and, in some cases, obtain explicit expressions for the sign of a target edge in terms of the observational covariance matrix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08311 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems van Seeventer, Gijs Salehkaleybar, Saber Statistics Theory Machine Learning We study identifiability in continuous-time linear stationary stochastic differential equations with known causal structure. Unlike existing approaches, we relax the assumption of a known diffusion matrix, thereby respecting the model's intrinsic scale invariance. Rather than recovering drift coefficients themselves, we introduce edge-sign identifiability: for a given causal structure, we ask whether the sign of a given drift entry is uniquely determined across all observational covariance matrices induced by parametrizations compatible with that structure. Under a notion of faithfulness, we derive criteria for characterising identifiability, non-identifiability, and partial identifiability for general graphs. Applying our criteria to specific causal structures, both analogous to classical causal settings (e.g., instrumental variables) and novel cyclic settings, we determine their edge-sign identifiability and, in some cases, obtain explicit expressions for the sign of a target edge in terms of the observational covariance matrix. |
| title | Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems |
| topic | Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2603.08311 |