Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders
This addresses the challenge of causal inference in complex real-world systems with non-linearities and confounding, though it is incremental as it builds on existing modular structural causal models.
The authors tackled the problem of causal discovery from data by developing a new algorithm that handles non-linear relations, latent confounders, cycles, and intervention data, demonstrating its performance on synthetic data.
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.