# Scalable Causal Discovery with Score Matching

arXiv: https://arxiv.org/abs/2304.03382 · HTML: https://mlsanity.com/paper/2304.03382/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 38 references that are in the map.
- First posted on arXiv 6 Apr 2023.

## Builds on (most cited first, 8 of 8)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data](https://mlsanity.com/paper/2006.10833/) (2020)
- [Inference via low-dimensional couplings](https://mlsanity.com/paper/1703.06131/) (2017)
- [Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting](https://mlsanity.com/paper/1711.00950/) (2017)
- [Obtaining Causal Information by Merging Datasets with MAXENT](https://mlsanity.com/paper/2107.07640/) (2021)

## Built on by (most cited first, 30 of 45)

- [General Identifiability and Achievability for Causal Representation Learning](https://mlsanity.com/paper/2310.15450/) (2023)
- [Assumption violations in causal discovery and the robustness of score matching](https://mlsanity.com/paper/2310.13387/) (2023)
- [textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discovery](https://mlsanity.com/paper/2306.10816/) (2023)
- [Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes](https://mlsanity.com/paper/2402.18477/) (2024)
- [Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling](https://mlsanity.com/paper/2310.18123/) (2023)
- [Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learning](https://mlsanity.com/paper/2406.14302/) (2024)
- [Score matching through the roof: linear, nonlinear, and latent variables causal discovery](https://mlsanity.com/paper/2407.18755/) (2024)
- [DCILP: A Distributed Approach for Large-Scale Causal Structure Learning](https://mlsanity.com/paper/2406.10481/) (2024)
- [A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery](https://mlsanity.com/paper/2410.06407/) (2024)
- [Identifiability Guarantees for Causal Disentanglement from Purely Observational Data](https://mlsanity.com/paper/2410.23620/) (2024)
- [Scalable and Flexible Causal Discovery with an Efficient Test for Adjacency](https://mlsanity.com/paper/2406.09177/) (2024)
- [Distinguishing Cause from Effect with Causal Velocity Models](https://mlsanity.com/paper/2502.05122/) (2025)
- [Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Models](https://mlsanity.com/paper/2405.14496/) (2024)
- [Causal Representation Learning from General Environments under Nonparametric Mixing](https://mlsanity.com/paper/2604.23800/) (2026)
- [Learning Causal Graphs via Monotone Triangular Transport Maps](https://mlsanity.com/paper/2305.18210/) (2023)
- [Shortcuts for causal discovery of nonlinear models by score matching](https://mlsanity.com/paper/2310.14246/) (2023)
- [AcceleratedLiNGAM: Learning Causal DAGs at the speed of GPUs](https://mlsanity.com/paper/2403.03772/) (2024)
- [Differentiable Bayesian Structure Learning with Acyclicity Assurance](https://mlsanity.com/paper/2309.01392/) (2023)
- [Cross-validating causal discovery via Leave-One-Variable-Out](https://mlsanity.com/paper/2411.05625/) (2024)
- [Score-matching-based Structure Learning for Temporal Data on Networks](https://mlsanity.com/paper/2412.07469/) (2024)
- [Causal Ordering for Structure Learning from Time Series](https://mlsanity.com/paper/2510.24639/) (2025)
- [DAG-FM: A Foundation Model for Causal Discovery under Heterogeneous Causal Mechanisms](https://mlsanity.com/paper/2607.11510/) (2026)
- [LoSAM: Local Search in Additive Noise Models with Mixed Mechanisms and General Noise for Global Causal Discovery](https://mlsanity.com/paper/2410.11759/) (2024)
- [Causal Order Discovery based on Monotonic SCMs](https://mlsanity.com/paper/2410.19870/) (2024)
- [Causal Discovery via Bayesian Optimization](https://mlsanity.com/paper/2501.14997/) (2025)
- [Your Assumed DAG is Wrong and Here's How To Deal With It](https://mlsanity.com/paper/2502.17030/) (2025)
- [When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discovery](https://mlsanity.com/paper/2506.23374/) (2025)
- [Ordering-based Causal Discovery via Generalized Score Matching](https://mlsanity.com/paper/2601.16249/) (2026)
- [Optimization-Free Topological Sort for Causal Discovery via the Schur Complement of Score Jacobians](https://mlsanity.com/paper/2604.25295/) (2026)
- [Learning Causal Orderings for In-Context Tabular Prediction](https://mlsanity.com/paper/2605.22335/) (2026)

## Abstract (arXiv)

This paper demonstrates how to discover the whole causal graph from the second derivative of the log-likelihood in observational non-linear additive Gaussian noise models. Leveraging scalable machine learning approaches to approximate the score function nabla log p(X), we extend the work of Rolland et al. (2022) that only recovers the topological order from the score and requires an expensive pruning step removing spurious edges among those admitted by the ordering. Our analysis leads to DAS (acronym for Discovery At Scale), a practical algorithm that reduces the complexity of the pruning by a factor proportional to the graph size. In practice, DAS achieves competitive accuracy with current state-of-the-art while being over an order of magnitude faster. Overall, our approach enables principled and scalable causal discovery, significantly lowering the compute bar.