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We address the problem of causal discovery from data, making use of therecently 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 additionalstructure, and extend the concept of {\sigma}-separation, the appropriategeneralization of the well-known notion of d-separation in this setting, toapply to {\sigma}-CGs. We prove the closedness of {\sigma}-separation undermarginalisation and conditioning and exploit this to implement a test of{\sigma}-separation on a {\sigma}-CG. This then leads us to the first causaldiscovery algorithm that can handle non-linear functional relations, latentconfounders, cyclic causal relationships, and data from different (stochastic)perfect interventions. As a proof of concept, we show on synthetic data howwell the algorithm recovers features of the causal graph of modular structuralcausal models.

Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders