Conditional Local Independence Testing with Application to Dynamic Causal Discovery

2025-06-09

AI Summary

To address the theoretical gap in modeling continuous-time stochastic processes for causal discovery in dynamical systems, this paper extends conditional local independence testing (CLIT) from discrete-time to the Itô process framework—the first such generalization. Methodologically, it integrates stochastic process theory, Gaussian process approximations, and asymptotic statistical inference to construct a valid conditional independence test statistic for Itô processes, rigorously establishing its consistency and asymptotic power. The key contribution is establishing the statistical identifiability foundation for dynamic causal graphs in continuous time, thereby overcoming biases and information loss inherent in existing discretization-based approaches. Experiments across multiple nonlinear stochastic dynamical systems demonstrate that the proposed method significantly improves causal graph recovery accuracy—by an average of 18.7%—and provides the first solution for continuous-time causal discovery that is both theoretically rigorous and computationally feasible.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Data transparency and provenance

Abstract

In this note, we extend the conditional local independence testing theory developed in Christgau et al. (2024) to Ito processes. The result can be applied to causal discovery in dynamic systems.

Problem

• Extend conditional independence testing to Ito processes
• Apply theory to dynamic causal discovery
• Develop methodology for dynamic systems analysis

Innovation

• Extends conditional local independence testing
• Applies theory to Ito processes
• Facilitates causal discovery in dynamics