摘要：

因果自回归流模型已经在非独立噪声等场景的因果方向推断问题上取得了一定的进展，但在多个结点的场景下仍存在全局结构搜索带来的准确度低和计算时间复杂度高的问题。面向非时序观察数据设计一种两阶段因果结构学习算法。在第一阶段，基于观测数据的条件独立性，对完全无向图通过条件独立性检验得到基本的因果骨架；在第二阶段，基于因果自回归流模型，通过标准化流的方法计算骨架中每条无向边在不同方向上的边缘似然概率，进而通过比较边缘似然概率进行因果方向推断。实验结果表明：该算法在多组不同参数生成的仿真因果结构数据集上均有较好的表现，与现有的主流因果结构学习算法相比，F1值平均提升15%~28%；在真实因果结构数据集实验中，该算法能够较为完整准确地学习到变量间的因果关系，与主流的因果结构学习算法相比，F1值平均提升28%~48%，具有更强的鲁棒性。

关键词: 因果结构学习, 因果发现, 加性噪声模型, 因果自回归流模型, 标准化流

Abstract:

The causal autoregressive flow model has realized promising results on the causal direction inference problem when the noise is affected by parent nodes. However, to date, existing methods suffer from low accuracy and high computational cost due to the global structure search. Therefore, in this study, a two-stage causal structure learning algorithm is designed for non-temporal observation data. The first stage involves obtaining the basic causal skeleton based on the conditional independence of the observed data from a completely undirected graph, and the second stage involves inferring causal direction by using normalizing flow to compare the edge likelihood probability in different directions based on the causal autoregressive flow model. The experiments on the simulated data shows that the proposed algorithm outperforms the existing mainstream causal structure learning algorithm, and the F1 score of the proposed algorithm is 15%-28% higher than the baseline methods. Similarly on the real world data, when compared with the mainstream causal learning algorithms, the proposed algorithm can learn the causal relationship more completely and accurately, and the F1 score of the proposed algorithm is 28%-48% higher than the baseline methods. Experimental results demonstrate the stronger robustness of the proposed algorithm.

Key words: causal structure learning, causal discovery, additive noise model, causal autoregressive flow model, normalizing flow