# Consistent Bayesian causal discovery for structural equation models with equal error variances

arXiv: https://arxiv.org/abs/2509.15197 · HTML: https://mlsanity.com/paper/2509.15197/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 18 Sep 2025.

## Builds on (most cited first, 15 of 15)

- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [Causal Representation Learning from Multiple Distributions: A General Setting](https://mlsanity.com/paper/2402.05052/) (2024)
- [Structure Learning in Graphical Modeling](https://mlsanity.com/paper/1606.02359/) (2016)
- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions](https://mlsanity.com/paper/1301.6697/) (2013)
- [Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables](https://mlsanity.com/paper/1908.03932/) (2019)
- [Partition MCMC for inference on acyclic digraphs](https://mlsanity.com/paper/1504.05006/) (2015)
- [Causal Discovery with Heterogeneous Observational Data](https://mlsanity.com/paper/2201.12392/) (2022)
- [Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression](https://mlsanity.com/paper/1511.08963/) (2015)
- [Discovery and inference of a causal network with hidden confounding](https://mlsanity.com/paper/2309.09420/) (2023)
- [Posterior Graph Selection and Estimation Consistency for High-dimensional Bayesian DAG Models](https://mlsanity.com/paper/1611.01205/) (2016)
- [Functional Bayesian Networks for Discovering Causality from Multivariate Functional Data](https://mlsanity.com/paper/2210.12832/) (2022)
- [Minimax Posterior Convergence Rates and Model Selection Consistency in High-dimensional DAG Models based on Sparse Cholesky Factors](https://mlsanity.com/paper/1811.06198/) (2018)
- [Consistent DAG selection for Bayesian causal discovery under general error distributions](https://mlsanity.com/paper/2508.00993/) (2025)

## Built on by (most cited first, 1 of 1)

- [MARCEDES: Score-based causal discovery under non-Gaussianity with continuous optimization](https://mlsanity.com/paper/2609.30643/) (2026)

## Abstract (arXiv)

We consider the problem of recovering the true causal structure among a set of variables, generated by a linear acyclic structural equation model (SEM) with the error terms being independent, not necessarily Gaussian, and having equal variances. It is well-known that the true underlying directed acyclic graph (DAG) encoding the causal structure is uniquely identifiable under this assumption. Interestingly, in this setting, it further holds that the sum of minimum expected squared errors for every variable, while predicted by the best linear combination of its parent variables, is minimised if and only if the causal structure is represented by any supergraph of the true DAG. In this work, we propose a Bayesian DAG selection method, where the working model assumes Gaussian SEM with equal error variances, and employ independent g-priors on each set of SEM coefficients. Furthermore, we utilise the aforementioned key property to establish that the proposed method recovers the true graph consistently without any additional distributional assumption, and illustrate it with a simulation study.