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2016 Identifiability of directed Gaussian graphical models with one latent source
Dennis Leung, Mathias Drton, Hisayuki Hara
Electron. J. Statist. 10(1): 394-422 (2016). DOI: 10.1214/16-EJS1111


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.


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Dennis Leung. Mathias Drton. Hisayuki Hara. "Identifiability of directed Gaussian graphical models with one latent source." Electron. J. Statist. 10 (1) 394 - 422, 2016.


Received: 1 May 2015; Published: 2016
First available in Project Euclid: 24 February 2016

zbMATH: 1332.62172
MathSciNet: MR3466188
Digital Object Identifier: 10.1214/16-EJS1111

Primary: 62H05 , 62H25 , 62J05

Keywords: Covariance matrix , factor analysis , Graphical model , parameter identification , structural equation model

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.10 • No. 1 • 2016
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