# Causal Discovery with Continuous Additive Noise Models

arXiv: https://arxiv.org/abs/1309.6779 · HTML: https://mlsanity.com/paper/1309.6779/

## Key facts

- Cited by 255 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2013.

## Built on by (most cited first, 30 of 255)

- [Causal Confusion in Imitation Learning](https://mlsanity.com/paper/1905.11979/) (2019)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [A Clarification of the Nuances in the Fairness Metrics Landscape](https://mlsanity.com/paper/2106.00467/) (2021)
- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [Diffusion Models for Causal Discovery via Topological Ordering](https://mlsanity.com/paper/2210.06201/) (2022)
- [Identifiability of latent-variable and structural-equation models: from linear to nonlinear](https://mlsanity.com/paper/2302.02672/) (2023)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Ordering-Based Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/2105.06631/) (2021)
- [Learning latent causal graphs via mixture oracles](https://mlsanity.com/paper/2106.15563/) (2021)
- [DAGs with No Curl: An Efficient DAG Structure Learning Approach](https://mlsanity.com/paper/2106.07197/) (2021)
- [CausalPFN: Amortized Causal Effect Estimation via In-Context Learning](https://mlsanity.com/paper/2506.07918/) (2025)
- [Differentiable DAG Sampling](https://mlsanity.com/paper/2203.08509/) (2022)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Causal Discovery with Score Matching on Additive Models with Arbitrary Noise](https://mlsanity.com/paper/2304.03265/) (2023)
- [Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data](https://mlsanity.com/paper/2203.15756/) (2022)
- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Model](https://mlsanity.com/paper/2205.13085/) (2022)
- [Active Bayesian Causal Inference](https://mlsanity.com/paper/2206.02063/) (2022)
- [Identifying Weight-Variant Latent Causal Models](https://mlsanity.com/paper/2208.14153/) (2022)
- [BayesDAG: Gradient-Based Posterior Inference for Causal Discovery](https://mlsanity.com/paper/2307.13917/) (2023)
- [Causal Representation Learning Made Identifiable by Grouping of Observational Variables](https://mlsanity.com/paper/2310.15709/) (2023)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [Stable Differentiable Causal Discovery](https://mlsanity.com/paper/2311.10263/) (2023)
- [Unifying Causal Representation Learning with the Invariance Principle](https://mlsanity.com/paper/2409.02772/) (2024)
- [Assumption violations in causal discovery and the robustness of score matching](https://mlsanity.com/paper/2310.13387/) (2023)

## Abstract (arXiv)

We consider the problem of learning causal directed acyclic graphs from an observational joint distribution. One can use these graphs to predict the outcome of interventional experiments, from which data are often not available. We show that if the observational distribution follows a structural equation model with an additive noise structure, the directed acyclic graph becomes identifiable from the distribution under mild conditions. This constitutes an interesting alternative to traditional methods that assume faithfulness and identify only the Markov equivalence class of the graph, thus leaving some edges undirected. We provide practical algorithms for finitely many samples, RESIT (Regression with Subsequent Independence Test) and two methods based on an independence score. We prove that RESIT is correct in the population setting and provide an empirical evaluation.