A Non-Euclidean Causal Discovery Algorithm in Metric Spaces
Fan Kuai, Jing Bing Yang · 2023
Causal information is implicit in the spatial characteristics of non-Euclidean data, and recently some researchers have proposed the Non-Euclidean Causal Model (NECM) to describe causal relationships in non-Euclidean data generation. In this paper, we first introduce distance covariance as the criterion for independence testing in the NECM and subsequently define strong or weak correlations between tensor variables containing potential causal relationships. Secondly, we propose a novel causal structure learning algorithm called Distance Covariance-based Non-Euclidean Hybrid Learning (D-NEHL), which can learn causal networks for non-Euclidean data in metric spaces. Finally, we conduct experiments on both simulated data and real stock market data. The results demonstrate that the D-NEHL algorithm exhibits higher accuracy and time performance compared to existing non-Euclidean causal learning methods. It is applicable to various types of non-Euclidean datasets and performs well on traditional Euclidean datasets.