Wang, Bingling; Zhou, Qing Causal network learning with non-invertible functional relationships. (English) Zbl 1510.62106 Comput. Stat. Data Anal. 156, Article ID 107141, 18 p. (2021). Summary: Discovery of causal relationships from observational data is an important problem in many areas. Several recent results have established the identifiability of causal directed acyclic graphs (DAGs) with non-Gaussian and/or nonlinear structural equation models (SEMs). Focusing on nonlinear SEMs defined by non-invertible functions, which exist in many data domains, a novel test is proposed for non-invertible bivariate causal models. Algorithms are further developed to incorporate this test in structure learning of DAGs that contain both linear and nonlinear causal relations. Extensive numerical comparisons show that the proposed algorithms outperform existing DAG learning methods in identifying causal graphical structures. The practical application of the methods is illustrated by learning causal networks for combinatorial binding of transcription factors from ChIP-Seq data. MSC: 62D20 Causal inference from observational studies 68T05 Learning and adaptive systems in artificial intelligence Keywords:causal discovery; directed acyclic graph; structural equation model; nonlinearity; non-invertible relation Software:DirectLiNGAM; sparsebn; TETRAD; bnlearn PDFBibTeX XMLCite \textit{B. Wang} and \textit{Q. Zhou}, Comput. Stat. Data Anal. 156, Article ID 107141, 18 p. (2021; Zbl 1510.62106) Full Text: DOI arXiv References: [1] Aragam, Bryon; Gu, Jiaying; Zhou, Qing, Learning large-scale Bayesian networks with the sparsebn package, J. Stat. Softw., 91, 11, 1-38 (2019) [2] Aragam, Bryon; Zhou, Qing, Concave penalized estimation of sparse Gaussian Bayesian networks, J. Mach. Learn. 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