# Assumption violations in causal discovery and the robustness of score matching

arXiv: https://arxiv.org/abs/2310.13387 · HTML: https://mlsanity.com/paper/2310.13387/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 55 references that are in the map.
- First posted on arXiv 20 Oct 2023.

## Builds on (most cited first, 20 of 20)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Causal Structure Learning](https://mlsanity.com/paper/1706.09141/) (2017)
- [High-recall causal discovery for autocorrelated time series with latent confounders](https://mlsanity.com/paper/2007.01884/) (2020)
- [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)
- [Invariant Causal Prediction for Sequential Data](https://mlsanity.com/paper/1706.08058/) (2017)
- [Gradient Estimators for Implicit Models](https://mlsanity.com/paper/1705.07107/) (2017)
- [Scalable Causal Discovery with Score Matching](https://mlsanity.com/paper/2304.03382/) (2023)
- [Causal Discovery with Score Matching on Additive Models with Arbitrary Noise](https://mlsanity.com/paper/2304.03265/) (2023)
- [Fast Conditional Independence Test for Vector Variables with Large Sample Sizes](https://mlsanity.com/paper/1804.02747/) (2018)
- [Evaluating structure learning algorithms with a balanced scoring function](https://mlsanity.com/paper/1905.12666/) (2019)
- [Causal Discovery in the Presence of Measurement Error: Identifiability Conditions](https://mlsanity.com/paper/1706.03768/) (2017)
- [Comparative Benchmarking of Causal Discovery Techniques](https://mlsanity.com/paper/1708.06246/) (2017)

## Built on by (most cited first, 28 of 28)

- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [CausalRivers -- Scaling up benchmarking of causal discovery for real-world time-series](https://mlsanity.com/paper/2503.17452/) (2025)
- [Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes](https://mlsanity.com/paper/2402.18477/) (2024)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Demystifying amortized causal discovery with transformers](https://mlsanity.com/paper/2405.16924/) (2024)
- [Amortized Active Causal Induction with Deep Reinforcement Learning](https://mlsanity.com/paper/2405.16718/) (2024)
- [Score matching through the roof: linear, nonlinear, and latent variables causal discovery](https://mlsanity.com/paper/2407.18755/) (2024)
- [A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery](https://mlsanity.com/paper/2410.06407/) (2024)
- [Better Simulations for Validating Causal Discovery with the DAG-Adaptation of the Onion Method](https://mlsanity.com/paper/2405.13100/) (2024)
- [Scalable and Flexible Causal Discovery with an Efficient Test for Adjacency](https://mlsanity.com/paper/2406.09177/) (2024)
- [Position: Causal Machine Learning Requires Rigorous Synthetic Experiments for Broader Adoption](https://mlsanity.com/paper/2508.08883/) (2025)
- [Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Models](https://mlsanity.com/paper/2405.14496/) (2024)
- [Deriving Causal Order from Single-Variable Interventions: Guarantees & Algorithm](https://mlsanity.com/paper/2405.18314/) (2024)
- [Challenges and Considerations in the Evaluation of Bayesian Causal Discovery](https://mlsanity.com/paper/2406.03209/) (2024)
- [Causal Representation Learning from General Environments under Nonparametric Mixing](https://mlsanity.com/paper/2604.23800/) (2026)
- [Shortcuts for causal discovery of nonlinear models by score matching](https://mlsanity.com/paper/2310.14246/) (2023)
- [The Robustness of Differentiable Causal Discovery in Misspecified Scenarios](https://mlsanity.com/paper/2510.12503/) (2025)
- [Efficient Differentiable Discovery of Causal Order](https://mlsanity.com/paper/2410.08787/) (2024)
- [Causal Ordering for Structure Learning from Time Series](https://mlsanity.com/paper/2510.24639/) (2025)
- [LoSAM: Local Search in Additive Noise Models with Mixed Mechanisms and General Noise for Global Causal Discovery](https://mlsanity.com/paper/2410.11759/) (2024)
- [Transformer Is Inherently a Causal Learner](https://mlsanity.com/paper/2601.05647/) (2026)
- [Ordering-based Causal Discovery via Generalized Score Matching](https://mlsanity.com/paper/2601.16249/) (2026)
- [ReBeCA: Unveiling Interpretable Behavior Hierarchy behind the Iterative Self-Reflection of Language Models with Causal Analysis](https://mlsanity.com/paper/2602.06373/) (2026)
- [Adaptive-CaRe: Adaptive Causal Regularization for Robust Outcome Prediction](https://mlsanity.com/paper/2602.06611/) (2026)
- [Causal-Audit: A Framework for Risk Assessment of Assumption Violations in Time-Series Causal Discovery](https://mlsanity.com/paper/2604.02488/) (2026)
- [Causal Learning with the Invariance Principle](https://mlsanity.com/paper/2605.13589/) (2026)
- [NetCause: Counterfactual Learning for Root Cause Analysis in Large-Scale Networks](https://mlsanity.com/paper/2606.13543/) (2026)
- [How Does Bayesian Causal Discovery Fail? Characterising Structural Consequences in Linear Gaussian Networks under Latent Confounding](https://mlsanity.com/paper/2607.09449/) (2026)

## Abstract (arXiv)

When domain knowledge is limited and experimentation is restricted by ethical, financial, or time constraints, practitioners turn to observational causal discovery methods to recover the causal structure, exploiting the statistical properties of their data. Because causal discovery without further assumptions is an ill-posed problem, each algorithm comes with its own set of usually untestable assumptions, some of which are hard to meet in real datasets. Motivated by these considerations, this paper extensively benchmarks the empirical performance of recent causal discovery methods on observational i.i.d. data generated under different background conditions, allowing for violations of the critical assumptions required by each selected approach. Our experimental findings show that score matching-based methods demonstrate surprising performance in the false positive and false negative rate of the inferred graph in these challenging scenarios, and we provide theoretical insights into their performance. This work is also the first effort to benchmark the stability of causal discovery algorithms with respect to the values of their hyperparameters. Finally, we hope this paper will set a new standard for the evaluation of causal discovery methods and can serve as an accessible entry point for practitioners interested in the field, highlighting the empirical implications of different algorithm choices.