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.