Assimilative Causal Inference

2025-05-20

AI Summary

Existing time-series causal inference methods struggle to jointly characterize instantaneous causal relationships and their dynamically evolving causal influence ranges (CIRs), particularly under high-dimensional settings, short sample lengths, or missing data. This paper proposes Assimilation-based Causal Inference (ACI), the first framework that formulates causal inference as a Bayesian data assimilation inverse problem. ACI reconstructs both instantaneous causal directions and time-varying CIRs from a single observation of only a subset of state variables. Its four key innovations are: (i) time-varying causal roles, (ii) no requirement for observations of candidate cause variables, (iii) mathematically provable CIR identification, and (iv) intrinsic scalability to high-dimensional systems and robustness to short or incomplete time series. Extensive validation on complex dynamical systems featuring intermittency and extreme events demonstrates that ACI significantly improves accuracy and robustness in instantaneous causal discovery.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Identifies instantaneous causal relationships dynamically
• Solves inverse causality via Bayesian data assimilation
• Scalable to high-dimensional systems with short data

Innovation

• Uses Bayesian data assimilation for inverse causality tracing
• Dynamically identifies shifting cause-effect roles over time
• Scalable to high-dimensional systems with efficient computation