# Identifiability of Gaussian Structural Equation Models with Dependent Errors Having Equal Variances

arXiv: https://arxiv.org/abs/1806.08156 · HTML: https://mlsanity.com/paper/1806.08156/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2018.

## Built on by (most cited first, 2 of 2)

- [Discovering Dynamic Causal Space for DAG Structure Learning](https://mlsanity.com/paper/2306.02822/) (2023)
- [Structural transfer learning of non-Gaussian DAG](https://mlsanity.com/paper/2310.10239/) (2023)

## Abstract (arXiv)

In this paper, we prove that some Gaussian structural equation models with dependent errors having equal variances are identifiable from their corresponding Gaussian distributions. Specifically, we prove identifiability for the Gaussian structural equation models that can be represented as Andersson-Madigan-Perlman chain graphs (Andersson et al., 2001). These chain graphs were originally developed to represent independence models. However, they are also suitable for representing causal models with additive noise (Pe~na, 2016. Our result implies then that these causal models can be identified from observational data alone. Our result generalizes the result by Peters and B"uhlmann (2014), who considered independent errors having equal variances. The suitability of the equal error variances assumption should be assessed on a per domain basis.