18 research outputs found
Identifiability of Gaussian structural equation models with equal error variances
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