Negative binomial graphical model with excess zeros

Markov random field or undirected graphical models (GM) are a popular class of GM useful in various fields because they provide an intuitive and interpretable graph expressing the complex relationship between random variables. The zero‐inflated local Poisson graphical model has been proposed as a graphical model for count data with excess zeros. However, as count data are often characterized by over‐dispersion, the local Poisson graphical model may suffer from a poor fit to data. In this paper, we propose a zero‐inflated local negative binomial (NB) graphical model. Due to the dependencies of parameters in our models, a direct optimization of the objective function is difficult. Instead, we devise expectation‐minimization algorithms based on two different parametrizations for the NB distribution. Through a simulation study, we illustrate the effectiveness of our method for learning network structure from over‐dispersed count data with excess zeros. We further apply our method to real data to estimate its network structure.