On Graphical Models via Univariate Exponential Family Distributions
On Graphical Models via Univariate Exponential Family Distributions
复制标题
DOI：
--
复制
发表时间：
2013-01
期刊：
影响因子：
--
通讯作者：
Eunho Yang;Pradeep Ravikumar;Genevera I. Allen;Zhandong Liu
中科院分区：
文献类型：
--
作者：
Eunho Yang;Pradeep Ravikumar;Genevera I. Allen;Zhandong Liu
无向图形模型，或马尔可夫网络，是一类流行的统计模型，用于广泛的各种应用。这一类的常见实例包括高斯图形模型和伊辛模型。然而，在许多设置中，可能不清楚使用哪个子类的图形模型，特别是对于非高斯和非分类数据。在这篇文章中，我们考虑了一类图模型的一般子类，其中节点条件分布来自指数族。这使我们能够从单变量指数族分布(如泊松分布、负二项分布和指数分布)中推导出多元图形模型分布。我们的主要贡献包括一类适合这些图模型分布的M-估计量；以及严格的统计分析表明，这些M-估计量以高概率准确地恢复了真实的图模型结构。我们提供了通过从泊松分布和指数分布导出的我们类别的图形模型的实例学习的基因组和蛋白质组网络的例子。
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly for non-Gaussian and non-categorical data. In this paper, we consider a general sub-class of graphical models where the node-wise conditional distributions arise from exponential families. This allows us to derive multivariate graphical model distributions from univariate exponential family distributions, such as the Poisson, negative binomial, and exponential distributions. Our key contributions include a class of M-estimators to fit these graphical model distributions; and rigorous statistical analysis showing that these M-estimators recover the true graphical model structure exactly, with high probability. We provide examples of genomic and proteomic networks learned via instances of our class of graphical models derived from Poisson and exponential distributions.