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An Additive Graphical Model for Discrete Data
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DOI：10.1080/01621459.2022.2119983.png)
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We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three-way statistical relation that shares similar properties with conditional independence by satisfying the semi-graphoid axioms. Based on this relation we build an additive graphical model for discrete variables that does not suffer from the restriction of a parametric model such as the Ising model. We develop an estimator of the new graphical model via the penalized estimation of the discrete version of the additive precision operator and establish the consistency of the estimator under the ultrahigh-dimensional setting. Along with these methodological developments, we also exploit the properties of discrete random variables to uncover a deeper relation between additive conditional independence and conditional independence than previously known. The new graphical model reduces to a conditional independence graphical model under certain sparsity conditions. We conduct simulation experiments and analysis of an HIV antiretroviral therapy dataset to compare the new method with existing ones. for this article are available online.
Keyword:
Additive conditional independence
Additive precision operator
Conditional independence
Discrete graphical model
Ising model
Ultrahigh-dimensional asymptotics
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3
论文数:
5.2K
被引数:
4.8W
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