Electronic Journal of Statistics

Identifiability of directed Gaussian graphical models with one latent source

Dennis Leung, Mathias Drton, and Hisayuki Hara

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We study parameter identifiability of directed Gaussian graphical models with one latent variable. In the scenario we consider, the latent variable is a confounder that forms a source node of the graph and is a parent to all other nodes, which correspond to the observed variables. We give a graphical condition that is sufficient for the Jacobian matrix of the parametrization map to be full rank, which entails that the parametrization is generically finite-to-one, a fact that is sometimes also referred to as local identifiability. We also derive a graphical condition that is necessary for such identifiability. Finally, we give a condition under which generic parameter identifiability can be determined from identifiability of a model associated with a subgraph. The power of these criteria is assessed via an exhaustive algebraic computational study for small models with 4, 5, and 6 observable variables, and a simulation study for large models with 25 or 35 observable variables.

Article information

Electron. J. Statist., Volume 10, Number 1 (2016), 394-422.

Received: May 2015
First available in Project Euclid: 24 February 2016

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Zentralblatt MATH identifier

Primary: 62H05: Characterization and structure theory 62H25: Factor analysis and principal components; correspondence analysis 62J05: Linear regression

Covariance matrix factor analysis graphical model parameter identification structural equation model


Leung, Dennis; Drton, Mathias; Hara, Hisayuki. Identifiability of directed Gaussian graphical models with one latent source. Electron. J. Statist. 10 (2016), no. 1, 394--422. doi:10.1214/16-EJS1111. https://projecteuclid.org/euclid.ejs/1456322680

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