Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems
For researchers in causal inference and dynamical systems, this work relaxes the assumption of known diffusion matrix and introduces partial identifiability, but the results are incremental as they extend existing identifiability concepts to a specific continuous-time linear setting.
This paper studies sign identifiability of causal effects in continuous-time linear stationary stochastic differential equations with known causal structure but unknown diffusion matrix, introducing a trichotomy of identifiable, non-identifiable, and partially identifiable edge signs. Criteria for membership in each category are derived under faithfulness, and applied to both classical and novel cyclic causal structures.
We study identifiability in continuous-time linear stationary stochastic differential equations with a known causal structure. Unlike existing approaches, we relax the assumption of a known diffusion matrix, thereby respecting the model's intrinsic scale invariance. Therefore, 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 parametrisations compatible with that structure. This leads to a trichotomy of edge-sign identifiability: identifiable, non-identifiable, and partially identifiable. This trichotomy introduces the new notion of partial identifiability to the literature, which we show is a genuine category in our setting. Under a notion of faithfulness, we derive criteria to identify membership of each category 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.