Identifiability of directed Gaussian graphical models with one latent source

Dennis Leung; Mathias Drton; Hisayuki Hara

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arXiv · 1505.01583

Identifiability of directed Gaussian graphical models with one latent source

Dennis Leung·Mathias Drton·Hisayuki Hara

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Abstract

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 on models with 4, 5, and 6 observable variables.

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Dennis Leung, Mathias Drton, Hisayuki Hara. 2015-05-07. Identifiability of directed Gaussian graphical models with one latent source. https://arxiv.org/abs/1505.01583

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