Identifiability of directed Gaussian graphical models with one latent source
Identifiability of directed Gaussian graphical models with one latent source
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DOI：
10.1214/16-ejs1111
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发表时间：
2015-05
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影响因子：
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通讯作者：
Dennis Leung;M. Drton;Hisayuki Hara
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文献类型：
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作者：
Dennis Leung;M. Drton;Hisayuki Hara
研究了具有一个潜变量的有向高斯图模型的参数可辨识性。在我们考虑的场景中，潜变量是一个混淆因素，它形成了图的源节点，并且是所有其他节点的父节点，这些节点对应于观察到的变量。我们给出了一个图形条件，这是足够的参数化映射的雅可比矩阵是满秩的，这意味着参数化一般是有限到一个，有时也被称为局部可识别性的事实。我们还推导出一个图形的条件，是必要的，这样的可识别性。最后，我们给出了一个条件，在该条件下可以根据与子图相关的模型的可识别性来确定类属参数的可识别性。这些标准的力量进行评估，通过一个详尽的代数计算研究模型与4，5，和6个可观察的变量。
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.