Telling cause from effect in deterministic linear dynamical systems

TL;DR

This paper introduces a novel method for causal inference in deterministic linear systems by leveraging spectral independence assumptions, enabling cause-effect determination from time series data without relying on noise.

Contribution

It proposes a new spectral-based approach for causal inference that exploits independence between the cause's spectrum and the effect's transfer function, applicable to deterministic systems.

Findings

Method performs well on synthetic data

Encouraging results on real-world data

Provides a new perspective beyond noise-based causality

Abstract

Inferring a cause from its effect using observed time series data is a major challenge in natural and social sciences. Assuming the effect is generated by the cause trough a linear system, we propose a new approach based on the hypothesis that nature chooses the "cause" and the "mechanism that generates the effect from the cause" independent of each other. We therefore postulate that the power spectrum of the time series being the cause is uncorrelated with the square of the transfer function of the linear filter generating the effect. While most causal discovery methods for time series mainly rely on the noise, our method relies on asymmetries of the power spectral density properties that can be exploited even in the context of deterministic systems. We describe mathematical assumptions in a deterministic model under which the causal direction is identifiable with this approach. We also discuss the method's performance under the additive noise model and its relationship to Granger causality. Experiments show encouraging results on synthetic as well as real-world data. Overall, this suggests that the postulate of Independence of Cause and Mechanism is a promising principle for causal inference on empirical time series.