We address the problem of causal discovery from data, making use of the recently proposed causal modeling framework of modular structural causal models (mSCM) to handle cycles, latent confounders and non-linearities. We introduce {\sigma}-connection graphs ({\sigma}-CG), a new class of mixed graphs (containing undirected, bidirected and directed edges) with additional structure, and extend the concept of {\sigma}-separation, the appropriate generalization of the well-known notion of d-separation in this setting, to apply to {\sigma}-CGs. We prove the closedness of {\sigma}-separation under marginalisation and conditioning and exploit this to implement a test of {\sigma}-separation on a {\sigma}-CG. This then leads us to the first causal discovery algorithm that can handle non-linear functional relations, latent confounders, cyclic causal relationships, and data from different (stochastic) perfect interventions. As a proof of concept, we show on synthetic data how well the algorithm recovers features of the causal graph of modular structural causal models.

采用模块化结构因果模型(mSCM)，引入了sigma-connection graphs (sigma-CG)，成功实现了能够处理非线性功能关系、潜在混淆、循环因果关系和不同随机完美干预数据的因果发现算法。

基于约束的非线性结构因果模型发现：循环和潜在混淆变量