Assimilative Causal Inference
Marios Andreou, Nan Chen, Erik Bollt
TL;DR
The paper tackles the challenge of detecting instantaneous, time-varying causal relationships in complex dynamical systems from limited observations. It introduces Assimilative Causal Inference (ACI), which recasts causality as a Bayesian inverse problem by comparing smoother and filter posteriors and using relative entropy to declare instantaneous links. ACI further defines the Causal Influence Range (CIR) to quantify how far effects propagate in time, with objective CIR implemented via averaging over thresholds; online smoothing enables real time tracking and extends to conditional ACI to handle non-target variables. Demonstrations on nonlinear CGNS models, including a dyad with extreme events and an ENSO diversity model, show how CIR patterns reveal early triggering, indirect pathways, and regime-dependent causal structure. The framework is scalable to high dimensions, accommodates short time series, and preserves dynamical integrity, offering broad potential for climate science, neuroscience, and other complex systems.
Abstract
Causal inference determines cause-and-effect relationships between variables and has broad applications across disciplines. Traditional time-series methods often reveal causal links only in a time-averaged sense, while ensemble-based information transfer approaches detect the time evolution of short-term causal relationships but are typically limited to low-dimensional systems. In this paper, a new causal inference framework, called assimilative causal inference (ACI), is developed. Fundamentally different from the state-of-the-art methods, ACI uses a dynamical system and a single realization of a subset of the state variables to identify instantaneous causal relationships and the dynamic evolution of the associated causal influence range (CIR). Instead of quantifying how causes influence effects as done traditionally, ACI solves an inverse problem via Bayesian data assimilation, thus tracing causes backward from observed effects with an implicit Bayesian hypothesis. Causality is determined by assessing whether incorporating the information of the effect variables reduces the uncertainty in recovering the potential cause variables. ACI has several desirable features. First, it captures the dynamic interplay of variables, where their roles as causes and effects can shift repeatedly over time. Second, a mathematically justified objective criterion determines the CIR without empirical thresholds. Third, ACI is scalable to high-dimensional problems by leveraging computationally efficient Bayesian data assimilation techniques. Finally, ACI applies to short time series and incomplete datasets. Notably, ACI does not require observations of candidate causes, which is a key advantage since potential drivers are often unknown or unmeasured. The effectiveness of ACI is demonstrated by complex dynamical systems showcasing intermittency and extreme events.