# On Causal Discovery with Equal Variance Assumption

arXiv: https://arxiv.org/abs/1807.03419 · HTML: https://mlsanity.com/paper/1807.03419/

## Key facts

- Cited by 59 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2018.

## Built on by (most cited first, 30 of 59)

- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Diffusion Models for Causal Discovery via Topological Ordering](https://mlsanity.com/paper/2210.06201/) (2022)
- [DAGs with No Curl: An Efficient DAG Structure Learning Approach](https://mlsanity.com/paper/2106.07197/) (2021)
- [A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Models](https://mlsanity.com/paper/2303.18211/) (2023)
- [textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discovery](https://mlsanity.com/paper/2306.10816/) (2023)
- [Optimal estimation of Gaussian DAG models](https://mlsanity.com/paper/2201.10548/) (2022)
- [Optimizing NOTEARS Objectives via Topological Swaps](https://mlsanity.com/paper/2305.17277/) (2023)
- [Adjustment Identification Distance: A gadjid for Causal Structure Learning](https://mlsanity.com/paper/2402.08616/) (2024)
- [Efficient Bayesian network structure learning via local Markov boundary search](https://mlsanity.com/paper/2110.06082/) (2021)
- [Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential families](https://mlsanity.com/paper/2110.04719/) (2021)
- [Valid Inference After Causal Discovery](https://mlsanity.com/paper/2208.05949/) (2022)
- [Global Optimality in Bivariate Gradient-based DAG Learning](https://mlsanity.com/paper/2306.17378/) (2023)
- [Effective Causal Discovery under Identifiable Heteroscedastic Noise Model](https://mlsanity.com/paper/2312.12844/) (2023)
- [Unitless Unrestricted Markov-Consistent SCM Generation: Better Benchmark Datasets for Causal Discovery](https://mlsanity.com/paper/2503.17037/) (2025)
- [Heteroscedastic Causal Structure Learning](https://mlsanity.com/paper/2307.07973/) (2023)
- [Learning linear non-Gaussian directed acyclic graph with diverging number of nodes](https://mlsanity.com/paper/2111.00740/) (2021)
- [Structural restrictions in local causal discovery: identifying direct causes of a target variable](https://mlsanity.com/paper/2307.16048/) (2023)
- [Order-based Structure Learning with Normalizing Flows](https://mlsanity.com/paper/2308.07480/) (2023)
- [Causal Representation Learning from General Environments under Nonparametric Mixing](https://mlsanity.com/paper/2604.23800/) (2026)
- [Integer Programming for Learning Directed Acyclic Graphs from Non-identifiable Gaussian Models](https://mlsanity.com/paper/2404.12592/) (2024)
- [BUILD with Precision: Bottom-Up Inference of Linear DAGs](https://mlsanity.com/paper/2512.16111/) (2025)
- [Sequentially learning the topological ordering of causal directed acyclic graphs with likelihood ratio scores](https://mlsanity.com/paper/2202.01748/) (2022)
- [dotears: Scalable, consistent DAG estimation using observational and interventional data](https://mlsanity.com/paper/2305.19215/) (2023)
- [Differentiable Bayesian Structure Learning with Acyclicity Assurance](https://mlsanity.com/paper/2309.01392/) (2023)
- [Optimal estimation of Gaussian (poly)trees](https://mlsanity.com/paper/2402.06380/) (2024)
- [Reinforcement Learning for Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2408.13448/) (2024)
- [Learning Gaussian DAG Models without Condition Number Bounds](https://mlsanity.com/paper/2511.06164/) (2025)
- [Learning Sparse Fixed-Structure Gaussian Bayesian Networks](https://mlsanity.com/paper/2107.10450/) (2021)
- [Correcting Confounding via Random Selection of Background Variables](https://mlsanity.com/paper/2202.02150/) (2022)
- [Information Theoretically Optimal Sample Complexity of Learning Dynamical Directed Acyclic Graphs](https://mlsanity.com/paper/2308.16859/) (2023)

## Abstract (arXiv)

Prior work has shown that causal structure can be uniquely identified from observational data when these follow a structural equation model whose error terms have equal variances. We show that this fact is implied by an ordering among (conditional) variances. We demonstrate that ordering estimates of these variances yields a simple yet state-of-the-art method for causal structure learning that is readily extendable to high-dimensional problems.