On Data-Driven Computation of Information Transfer for Causal Inference in Dynamical Systems

TL;DR

This paper introduces a data-driven method to compute a new measure of information transfer that accurately captures causal interactions in dynamical systems using transfer operator theory.

Contribution

It demonstrates how to compute a novel causal information transfer measure from time-series data via transfer operator frameworks, improving causal inference accuracy.

Findings

Effective in linear and nonlinear systems

Outperforms traditional causality measures

Validated through multiple examples

Abstract

In this paper, we provide a novel approach to capture causal interaction in a dynamical system from time-series data. In \cite{sinha_IT_CDC2016}, we have shown that the existing measures of information transfer, namely directed information, granger causality and transfer entropy fail to capture true causal interaction in dynamical system and proposed a new definition of information transfer that captures true causal interaction. The main contribution of this paper is to show that the proposed definition of information transfer in \cite{sinha_IT_CDC2016}\cite{sinha_IT_ICC} can be computed from time-series data. We use transfer operator theoretic framework involving Perron-Frobenius and Koopman operators for the data-driven approximation of the system dynamics and for the computation of information transfer. Several examples involving linear and nonlinear system dynamics are presented to verify the efficiency of the developed algorithm.