Fractal Conditional Correlation Dimension Infers Complex Causal Networks

TL;DR

This paper introduces a geometric approach called $oGeoC$ for inferring complex causal networks from time series data, effectively distinguishing direct from indirect causal links with high accuracy.

Contribution

The paper presents the $oGeoC$ principle and two algorithms that utilize geometric information flow to accurately identify direct causal relations in complex networks.

Findings

Algorithms accurately identify direct causal links with low false positives.

Effective in coupled logistic networks with sufficient observations.

Provides a geometric interpretation for causal inference.

Abstract

Determining causal inference has become popular in physical and engineering applications. While the problem has immense challenges, it provides a way to model the complex networks by observing the time series. In this paper, we present the optimal conditional correlation dimensional geometric information flow principle ($oGeoC$) that can reveal direct and indirect causal relations in a network through geometric interpretations. We introduce two algorithms that utilize the $oGeoC$ principle to discover the direct links and then remove indirect links. The algorithms are evaluated using coupled logistic networks. The results indicate that when the number of observations is sufficient, the proposed algorithms are highly accurate in identifying direct causal links and have a low false positive rate.