Tangent Space Causal Inference: Leveraging Vector Fields for Causal Discovery in Dynamical Systems

TL;DR

This paper introduces TSCI, a novel method leveraging vector fields for causal discovery in dynamical systems, outperforming CCM and adaptable with deep learning enhancements.

Contribution

The paper presents TSCI, a model-agnostic causal inference method based on vector fields, improving accuracy over CCM and incorporating deep learning for enhanced performance.

Findings

TSCI outperforms CCM in standard dynamical systems.

Augmented TSCI with deep learning further improves causal detection.

TSCI is computationally efficient and versatile across benchmarks.

Abstract

Causal discovery with time series data remains a challenging yet increasingly important task across many scientific domains. Convergent cross mapping (CCM) and related methods have been proposed to study time series that are generated by dynamical systems, where traditional approaches like Granger causality are unreliable. However, CCM often yields inaccurate results depending upon the quality of the data. We propose the Tangent Space Causal Inference (TSCI) method for detecting causalities in dynamical systems. TSCI works by considering vector fields as explicit representations of the systems' dynamics and checks for the degree of synchronization between the learned vector fields. The TSCI approach is model-agnostic and can be used as a drop-in replacement for CCM and its generalizations. We first present a basic version of the TSCI algorithm, which is shown to be more effective than the basic CCM algorithm with very little additional computation. We additionally present augmented versions of TSCI that leverage the expressive power of latent variable models and deep learning. We validate our theory on standard systems, and we demonstrate improved causal inference performance across a number of benchmark tasks.