Deep Koopman operator framework for causal discovery in nonlinear dynamical systems

TL;DR

This paper introduces Kausal, a novel causal discovery algorithm for nonlinear dynamical systems using deep Koopman operator theory, enabling better understanding of complex cause-effect relationships in real-world phenomena.

Contribution

The paper develops a new causal discovery method leveraging deep Koopman operators and demonstrates its effectiveness over existing approaches, with real-world application to climate data.

Findings

Kausal outperforms existing methods in discovering causal signals.

The approach effectively characterizes cause-effect relationships in nonlinear systems.

Applied successfully to El Niño-Southern Oscillation data.

Abstract

We use a deep Koopman operator-theoretic formalism to develop a novel causal discovery algorithm, Kausal. Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. This presents a challenge in studying many real-world systems, such as the Earth's climate. Meanwhile, Koopman operator methods have emerged as a promising tool for approximating nonlinear dynamics in a linear space of observables. In Kausal, we propose to leverage this powerful idea for causal analysis where optimal observables are inferred using deep learning. Causal estimates are then evaluated in a reproducing kernel Hilbert space, and defined as the distance between the marginal dynamics of the effect and the joint dynamics of the cause-effect observables. Our numerical experiments demonstrate Kausal's superior ability in discovering and characterizing causal signals compared to existing approaches of prescribed observables. Lastly, we extend our analysis to observations of El Ni\~no-Southern Oscillation highlighting our algorithm's applicability to real-world phenomena. Our code is available at https://github.com/juannat7/kausal.