Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders
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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 σ-connection graphs (σ-CG), a new class of mixed graphs (containing undirected, bidirected and directed edges) with additional structure, and extend the concept of σ-separation, the appropriate generalization of the well-known notion of d-separation in this setting, to apply to σ-CGs. We prove the closedness of σ-separation under marginalisation and conditioning and exploit this to implement a test of σ-separation on a σ-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.
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