Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems

2026-03-09

AI Summary

This work addresses the problem of determining whether the sign of the drift coefficient associated with a specific edge in the causal graph of a continuous-time linear stationary stochastic differential equation is identifiable when the diffusion matrix is unknown. The authors introduce the notion of “edge sign identifiability” and develop a unified analytical framework that does not require prior knowledge of the diffusion matrix, thereby accommodating cyclic structures and classical causal models such as instrumental variables. By integrating causal graphical models with covariance matrix analysis, they derive general graphical criteria for sign identifiability—fully identifiable, non-identifiable, or partially identifiable—and provide explicit expressions for the target edge’s sign in terms of observed covariances for several canonical graph structures. This approach substantially relaxes the common assumption of known diffusion terms and broadens the applicability of sign inference for causal effects in continuous-time settings.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• sign identifiability
• causal effects
• stochastic dynamical systems
• stationary processes
• causal structure

Innovation

• edge-sign identifiability
• stochastic dynamical systems
• causal identifiability
• scale invariance
• stationary processes