# Learning Causal Graphs via Monotone Triangular Transport Maps

arXiv: https://arxiv.org/abs/2305.18210 · HTML: https://mlsanity.com/paper/2305.18210/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 26 May 2023.

## Builds on (most cited first, 15 of 15)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Linear Causal Disentanglement via Interventions](https://mlsanity.com/paper/2211.16467/) (2022)
- [Causal Discovery Toolbox: Uncover causal relationships in Python](https://mlsanity.com/paper/1903.02278/) (2019)
- [Structural Agnostic Modeling: Adversarial Learning of Causal Graphs](https://mlsanity.com/paper/1803.04929/) (2018)
- [Scalable Causal Discovery with Score Matching](https://mlsanity.com/paper/2304.03382/) (2023)
- [Inference via low-dimensional couplings](https://mlsanity.com/paper/1703.06131/) (2017)
- [Optimal transport for causal discovery](https://mlsanity.com/paper/2201.09366/) (2022)
- [A Kernel Independence Test for Random Processes](https://mlsanity.com/paper/1402.4501/) (2014)
- [Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting](https://mlsanity.com/paper/1711.00950/) (2017)

## Built on by (most cited first, 4 of 4)

- [Scalable Counterfactual Distribution Estimation in Multivariate Causal Models](https://mlsanity.com/paper/2311.00927/) (2023)
- [Optimal Transport for Structure Learning Under Missing Data](https://mlsanity.com/paper/2402.15255/) (2024)
- [On sample complexity of conditional independence testing with Von Mises estimator with application to causal discovery](https://mlsanity.com/paper/2310.13553/) (2023)
- [A friendly introduction to triangular transport](https://mlsanity.com/paper/2503.21673/) (2025)

## Abstract (arXiv)

We study the problem of causal structure learning from data using optimal transport (OT). Specifically, we first provide a constraint-based method which builds upon lower-triangular monotone parametric transport maps to design conditional independence tests which are agnostic to the noise distribution. We provide an algorithm for causal discovery up to Markov Equivalence with no assumptions on the structural equations/noise distributions, which allows for settings with latent variables. Our approach also extends to score-based causal discovery by providing a novel means for defining scores. This allows us to uniquely recover the causal graph under additional identifiability and structural assumptions, such as additive noise or post-nonlinear models. We provide experimental results to compare the proposed approach with the state of the art on both synthetic and real-world datasets.