Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems

TL;DR

This paper investigates when the signs of causal effects in continuous-time linear stochastic systems can be uniquely identified from observational data, relaxing previous assumptions and providing criteria for various graph structures.

Contribution

It introduces the concept of edge-sign identifiability for stationary stochastic systems, extending causal inference methods to more general models without assuming known diffusion matrices.

Findings

Derived criteria for identifiability, non-identifiability, and partial identifiability.

Applied criteria to classical and cyclic causal structures, determining sign identifiability.

Obtained explicit expressions for causal effect signs in certain models.

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.