Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems

• URL: http://arxiv.org/abs/2603.08311v1
• Date: Mon, 09 Mar 2026 12:33:51 GMT
• Title: Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems
• Abstract summary: We study identifiability in continuous-time linear stationary differential equations with known causal structure.<n>Under a notion of faithfulness, we derive criteria for characterising identifiability, non-identifiability, and partial identifiability for general graphs.
• Score: 7.097327421487074
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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.

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