NHCE: A Neural High-Order Causal Entropy Algorithm for Disentangling Coupling Dynamics

Inferring causality to disentangle coupling dynamics has always been a challenging task, yet to be fully addressed. Previous works achieve the identification of causal relationships between coupling variables with inter-individual interactions. However, the implementation for high-order multi-variable systems suffers from the problem of the curse of dimensionality. Thus, to address this issue, a novel algorithm, called Neural High-order Causal Entropy (NHCE), consisting of High-dimensional Bi-variate Mutual Information Neural Estimation (HB-MINE) and High-dimensional Conditional Mutual Information Neural Estimation (HC-MINE), is proposed in this work. Furthermore, benchmark experiments are conducted to show the improved performance on the application scenarios. To demonstrate the application value on revealing the causal mechanism in coupling dynamics, extensive experiments have been conducted on the collective motion datasets including pigeon flocks and dog groups. The results show that NHCE provides insightful anatomy of complex leaderships in these coupling dynamics.