Identifiability of Gaussian structural equation models with equal error variances
成果类型：
Article
署名作者：
Peters, J.; Buehlmann, P.
署名单位：
Swiss Federal Institutes of Technology Domain; ETH Zurich
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/ast043
发表日期：
2014
页码：
219228
关键词：
摘要：
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 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 in the case where all noise variables have the same variance: 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, then, assuming that all variables are observed, the causal structure can be inferred from observational data only. We propose a statistical method and an algorithm based on our theoretical findings.