Fractal Conditional Correlation Dimension Infers Complex Causal Networks

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.