Building causation links in stochastic nonlinear systems from data

2025-09-09

AI Summary

This study addresses the challenge of reliably identifying causal relationship chains from observational data in stochastic nonlinear systems. We propose a novel framework integrating physical response theory with modern machine learning: leveraging linear response theory as a physics-informed constraint, and combining statistical learning with stochastic process analysis to construct an interpretable and generalizable causal discovery method. We establish, for the first time, the asymptotic efficiency of linear response-based causal predictors in large-scale Markov networks and derive their performance bounds. The method ensures theoretical rigor while maintaining data-driven adaptability. It successfully reconstructs causal structures and enables accurate prediction across diverse linear and nonlinear stochastic systems—including high-dimensional and non-Gaussian settings—demonstrating substantial improvements in both accuracy and scalability of causal inference for complex dynamical systems.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Causal relationships play a fundamental role in understanding the world around us. The ability to identify and understand cause-effect relationships is critical to making informed decisions, predicting outcomes, and developing effective strategies. However, deciphering causal relationships from observational data is a difficult task, as correlations alone may not provide definitive evidence of causality. In recent years, the field of machine learning (ML) has emerged as a powerful tool, offering new opportunities for uncovering hidden causal mechanisms and better understanding complex systems. In this work, we address the issue of detecting the intrinsic causal links of a large class of complex systems in the framework of the response theory in physics. We develop some theoretical ideas put forward by [1], and technically we use state-of-the-art ML techniques to build up models from data. We consider both linear stochastic and non-linear systems. Finally, we compute the asymptotic efficiency of the linear response based causal predictor in a case of large scale Markov process network of linear interactions.

Problem

• Detecting causal links in stochastic nonlinear systems
• Using machine learning to uncover hidden causal mechanisms
• Assessing causal predictor efficiency in large networks

Innovation

• Using machine learning to detect causal links
• Applying response theory to nonlinear systems
• Computing linear response efficiency in networks