# Enabling Causal Discovery in Post-Nonlinear Models with Normalizing Flows

arXiv: https://arxiv.org/abs/2407.04980 · HTML: https://mlsanity.com/paper/2407.04980/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 42 references that are in the map.
- First posted on arXiv 6 Jul 2024.

## Builds on (most cited first, 17 of 17)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Diffusion Models for Causal Discovery via Topological Ordering](https://mlsanity.com/paper/2210.06201/) (2022)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [A polynomial-time algorithm for learning nonparametric causal graphs](https://mlsanity.com/paper/2006.11970/) (2020)
- [Computably Continuous Reinforcement-Learning Objectives are PAC-learnable](https://mlsanity.com/paper/2303.05518/) (2023)
- [Bayesian Network Structure Learning with Integer Programming: Polytopes, Facets, and Complexity](https://mlsanity.com/paper/1605.04071/) (2016)
- [Conditional Independence Testing via Latent Representation Learning](https://mlsanity.com/paper/2209.01547/) (2022)
- [Rank-Based Causal Discovery for Post-Nonlinear Models](https://mlsanity.com/paper/2302.12341/) (2023)

## Built on by (most cited first, 1 of 1)

- [DAGAF: A directed acyclic generative adversarial framework for joint structure learning and tabular data synthesis](https://mlsanity.com/paper/2604.04290/) (2026)

## Abstract (arXiv)

Post-nonlinear (PNL) causal models stand out as a versatile and adaptable framework for modeling intricate causal relationships. However, accurately capturing the invertibility constraint required in PNL models remains challenging in existing studies. To address this problem, we introduce CAF-PoNo (Causal discovery via Normalizing Flows for Post-Nonlinear models), harnessing the power of the normalizing flows architecture to enforce the crucial invertibility constraint in PNL models. Through normalizing flows, our method precisely reconstructs the hidden noise, which plays a vital role in cause-effect identification through statistical independence testing. Furthermore, the proposed approach exhibits remarkable extensibility, as it can be seamlessly expanded to facilitate multivariate causal discovery via causal order identification, empowering us to efficiently unravel complex causal relationships. Extensive experimental evaluations on both simulated and real datasets consistently demonstrate that the proposed method outperforms several state-of-the-art approaches in both bivariate and multivariate causal discovery tasks.