An additive graphical model for discrete data
This provides a more flexible tool for statistical analysis of discrete data, such as in medical studies like HIV therapy, but it is incremental as it builds on existing graphical model concepts.
The authors tackled the problem of modeling discrete data with graphical models by introducing a nonparametric additive graphical model that avoids the restrictions of parametric models like the Ising model, and they developed a consistent estimator for it under ultrahigh-dimensional settings.
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 data set to compare the new method with existing ones.