# Causal network learning with non-invertible functional relationships

arXiv: https://arxiv.org/abs/2004.09646 · HTML: https://mlsanity.com/paper/2004.09646/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2020.

## Built on by (most cited first, 6 of 6)

- [Distributed Learning of Generalized Linear Causal Networks](https://mlsanity.com/paper/2201.09194/) (2022)
- [ExMAG: Learning of Maximally Ancestral Graphs](https://mlsanity.com/paper/2503.08245/) (2025)
- [Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach](https://mlsanity.com/paper/2604.05829/) (2026)
- [Nonlinear Causal Discovery through a Sequential Edge Orientation Approach](https://mlsanity.com/paper/2506.05590/) (2025)
- [Hybrid Causal Identification and Causal Mechanism Clustering](https://mlsanity.com/paper/2507.21792/) (2025)
- [LxCIM: a new rank-based binary classifier performance metric invariant to local exchange of classes](https://mlsanity.com/paper/2512.10053/) (2025)

## Abstract (arXiv)

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.