Identifiability of Gaussian structural equation models with equal error variances

TL;DR

This paper proves that Gaussian structural equation models with equal error variances are fully identifiable from observational data, enabling causal inference without interventions, and proposes a method and algorithm based on this result.

Contribution

It establishes full identifiability of the causal graph in Gaussian SEMs with equal error variances, advancing causal inference methods.

Findings

Full identifiability of the causal graph under equal error variances.

A statistical method and algorithm exploiting the theoretical result.

Implications for causal inference from observational data.

Abstract

We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model, there is a directed acyclic graph describing the relationships between the variables. In Gaussian structural equation models with linear functions, the graph can be identified from the joint distribution only up to Markov equivalence classes, assuming faithfulness. In this work, we prove full identifiability if all noise variables have the same variances: the directed acyclic graph can be recovered from the joint Gaussian distribution. Our result has direct implications for causal inference: if the data follow a Gaussian structural equation model with equal error variances and assuming that all variables are observed, the causal structure can be inferred from observational data only. We propose a statistical method and an algorithm that exploit our theoretical findings.