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Discovery of causal relationships from observational data is an importantproblem in many areas. Several recent results have established theidentifiability of causal DAGs with non-Gaussian and/or nonlinear structuralequation models (SEMs). In this paper, we focus on nonlinear SEMs defined bynon-invertible functions, which exist in many data domains, and propose a noveltest for non-invertible bivariate causal models. We further develop a method toincorporate this test in structure learning of DAGs that contain both linearand nonlinear causal relations. By extensive numerical comparisons, we showthat our algorithms outperform existing DAG learning methods in identifyingcausal graphical structures. We illustrate the practical application of ourmethod in learning causal networks for combinatorial binding of transcriptionfactors from ChIP-Seq data.

Causal network learning with non-invertible functional relationships