Causal Structure Learning for Dynamical Systems with Theoretical Score Analysis

TL;DR

CaDyT is a new method for causal discovery in continuous-time dynamical systems that effectively handles irregular sampling and improves accuracy over existing approaches by using Gaussian Processes and a principled search strategy.

Contribution

It introduces CaDyT, a novel continuous-time causal discovery framework based on Difference models and Gaussian Process inference, addressing limitations of discretization and causality assumptions.

Findings

Outperforms state-of-the-art methods on irregularly sampled data

More accurately recovers true causal structures in dynamical systems

Effective in both regular and irregular sampling scenarios

Abstract

Real world systems evolve in continuous-time according to their underlying causal relationships, yet their dynamics are often unknown. Existing approaches to learning such dynamics typically either discretize time -- leading to poor performance on irregularly sampled data -- or ignore the underlying causality. We propose CaDyT, a novel method for causal discovery on dynamical systems addressing both these challenges. In contrast to state-of-the-art causal discovery methods that model the problem using discrete-time Dynamic Bayesian networks, our formulation is grounded in Difference-based causal models, which allow milder assumptions for modeling the continuous nature of the system. CaDyT leverages exact Gaussian Process inference for modeling the continuous-time dynamics which is more aligned with the underlying dynamical process. We propose a practical instantiation that identifies the causal structure via a greedy search guided by the Algorithmic Markov Condition and Minimum Description Length principle. Our experiments show that CaDyT outperforms state-of-the-art methods on both regularly and irregularly-sampled data, discovering causal networks closer to the true underlying dynamics.