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

By Patrick Forr'e, Joris M. Mooij. 2018

68 citations recorded by the source corpus.

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.

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Citations in the corpus

Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions (2017, methodology): “We will make use of the terminology of the recently proposed Joint Causal Inference (JCI) framework [Mooij et al., 2018].”
Foundations of structural causal models with cycles and latent variables (2016, methodology): “modular SCMs [18, 19] directly apply to the subclass of simple SCMs, as well.”
D’ya Like DAGs? A Survey on Structure Learning and Causal Discovery (2021, background): “Other types of graph used to represent causal structure include Partially Oriented Induced Path Graphs (POIPGs) [188, 223], Single World Intervention Graphs (SWIGs) [24, 197, 198], σ-connection graphs [57], undirected graphs [12], interaction and component graphs for dynamic systems [41], Maximal Al”
Causal Transfer Learning (2017, methodology): “usal graph or the intervention targets to be known. The method gives promising results on simulated data. It is straightforward to extend our method to the cyclic case by making use of the results by Forré and Mooij (2018). More work remains to be done on the implementation side, for example, scalin”
Joint Causal Inference from Multiple Contexts (2016, methodology): “The latter approach is commonly used by constraint-based methods for causal discovery from multiple data sets (e.g., Tillman, 2009; Claassen and Heskes, 2010; Tillman and Spirtes, 2011; Hyttinen et al., 2014; Triantafillou and Tsamardinos, 2015; Rothenhäusler et al., 2015; Forré and Mooij, 2018).”