# Demistifying Data and Simulator Assumptions in Supervised Causal Discovery

arXiv: https://arxiv.org/abs/2609.37446 · HTML: https://mlsanity.com/paper/2609.37446/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 54 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [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)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [Learning to Induce Causal Structure](https://mlsanity.com/paper/2204.04875/) (2022)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [Nested Markov Properties for Acyclic Directed Mixed Graphs](https://mlsanity.com/paper/1701.06686/) (2017)
- [Stable Differentiable Causal Discovery](https://mlsanity.com/paper/2311.10263/) (2023)
- [A Meta-Learning Approach to Bayesian Causal Discovery](https://mlsanity.com/paper/2412.16577/) (2024)
- [Sample, estimate, aggregate: A recipe for causal discovery foundation models](https://mlsanity.com/paper/2402.01929/) (2024)
- [Supervised Whole DAG Causal Discovery](https://mlsanity.com/paper/2006.04697/) (2020)
- [Reliable Causal Discovery with Improved Exact Search and Weaker Assumptions](https://mlsanity.com/paper/2201.05666/) (2022)
- [ML4C: Seeing Causality Through Latent Vicinity](https://mlsanity.com/paper/2110.00637/) (2021)
- [Demystifying amortized causal discovery with transformers](https://mlsanity.com/paper/2405.16924/) (2024)
- [Scalable Differentiable Causal Discovery in the Presence of Latent Confounders with Skeleton Posterior (Extended Version)](https://mlsanity.com/paper/2406.10537/) (2024)
- [Arrow: A Foundation Model for Causal Discovery](https://mlsanity.com/paper/2605.07204/) (2026)
- [Learning Causal Graphs at Scale: A Foundation Model Approach](https://mlsanity.com/paper/2506.18285/) (2025)
- [Learning Identifiable Structures Helps Avoid Bias in DNN-based Supervised Causal Learning](https://mlsanity.com/paper/2502.10883/) (2025)
- [Test-Time Learning of Causal Structure from Interventional Data](https://mlsanity.com/paper/2602.19131/) (2026)
- [A Knowledge-Informed Pretrained Model for Causal Discovery](https://mlsanity.com/paper/2603.20842/) (2026)
- [Test Time Training for Supervised Causal Learning](https://mlsanity.com/paper/2605.30015/) (2026)

## Abstract (arXiv)

Supervised causal discovery learns to infer causal structure for a new dataset from training datasets paired with structural labels. These training pairs are typically simulated, making the simulator both a source of supervision and a carrier of assumptions about causal graphs, mechanisms, and noise. Understanding the resulting predictions therefore requires examining how these assumptions supplement the information available in observational data, which may be compatible with multiple causal graphs. This paper examines that relationship across representative methods available through June 2026. We organize these methods by prediction target, prediction granularity, encoder, structural decoder, and training regime to relate what each method predicts to how it uses data and simulator-based supervision. Using this framework, we distinguish two questions: whether the target is identifiable under the assumed model class, and whether a trained predictor generalizes beyond its training distribution. Restrictions on mechanisms and noise can make otherwise ambiguous causal directions identifiable, but predictive accuracy under those restrictions does not establish transfer when they change. This distinction motivates evaluation that matches metrics to the identifiable graph target and tests changes in graphs, mechanisms, and noise between training and deployment. Extending such evaluation to real data also requires documenting the external causal evidence and uncertainty behind benchmark reference graphs. Together, these analyses guide method comparison and identify open questions in transfer, test-time adaptation, and uncertainty assessment.