Causal discovery based on heterogeneous non-Euclidean data

Causal relationships play an irreplaceable role in revealing the mechanisms of phenomena and guiding intervention actions. However, due to limitations in existing frameworks regarding model representations and learning algorithms, only a few studies have explored causal discovery on non-Euclidean data. In this paper, we address the issue by proposing a causal mapping process based on coordinate representations for heterogeneous non-Euclidean data. We propose a data generation mechanism between the parent nodes and the child nodes and create a causal mechanism based on multi-dimensional tensor regression. Furthermore, within the aforementioned theoretical framework, we propose a two-stage causal discovery approach based on regularized generalized canonical correlation analysis. Using the discrete representation in the shared projection direction, causal relationships between heterogeneous non-Euclidean variables can be discovered more accurately. Finally, empirical research is conducted on real-world industrial sensor data, which demonstrates the effectiveness of the proposed method for discovering causal relationships in heterogeneous non-Euclidean data. © 2024 Systems Engineering Society of China. All rights reserved.