Causal network learning with non-invertible functional relationships
This work addresses causal discovery in domains with non-invertible functional relationships, such as biological data, but appears incremental as it builds on existing nonlinear SEM frameworks.
The authors tackled the problem of learning causal networks from observational data by developing a novel test for non-invertible bivariate causal models and integrating it into DAG structure learning, showing that their algorithms outperform existing methods in identifying causal graphical structures.
Discovery of causal relationships from observational data is an important problem in many areas. Several recent results have established the identifiability of causal DAGs with non-Gaussian and/or nonlinear structural equation models (SEMs). In this paper, we focus on nonlinear SEMs defined by non-invertible functions, which exist in many data domains, and propose a novel test for non-invertible bivariate causal models. We further develop a method to incorporate this test in structure learning of DAGs that contain both linear and nonlinear causal relations. By extensive numerical comparisons, we show that our algorithms outperform existing DAG learning methods in identifying causal graphical structures. We illustrate the practical application of our method in learning causal networks for combinatorial binding of transcription factors from ChIP-Seq data.