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Negative binomial graphical model with excess zeros
Author(s) -
Park Beomjin,
Choi Hosik,
Park Changyi
Publication year - 2021
Publication title -
statistical analysis and data mining: the asa data science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.381
H-Index - 33
eISSN - 1932-1872
pISSN - 1932-1864
DOI - 10.1002/sam.11536
Subject(s) - graphical model , negative binomial distribution , count data , poisson distribution , markov random field , binomial (polynomial) , computer science , graph , markov chain , algorithm , zero inflated model , mathematics , theoretical computer science , statistics , artificial intelligence , poisson regression , population , demography , segmentation , sociology , image segmentation
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.