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.

中文翻译：

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具有多余零的负二项式图形模型

马尔可夫随机场或无向图模型 (GM) 是一种流行的 GM 类别，可用于各个领域，因为它们提供了一种直观且可解释的图来表达随机变量之间的复杂关系。零膨胀局部泊松图模型已被提议作为具有多余零的计数数据的图模型。但是，由于计数数据通常具有过度分散的特征，因此局部泊松图模型可能会与数据拟合不佳。在本文中，我们提出了一个零膨胀的局部负二项式（NB）图形模型。由于我们模型中参数的依赖性，目标函数的直接优化是困难的。相反，我们设计了基于 NB 分布的两种不同参数化的期望最小化算法。通过模拟研究，我们说明了我们的方法从具有过多零的过度分散的计数数据中学习网络结构的有效性。我们进一步将我们的方法应用于真实数据以估计其网络结构。