Mixed Graphical Models via Exponential Families
Mixed Graphical Models via Exponential Families
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发表时间：
2014
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通讯作者：
Eunho Yang;Yulia Baker;Pradeep Ravikumar;Genevera I. Allen;Zhandong Liu
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作者：
Eunho Yang;Yulia Baker;Pradeep Ravikumar;Genevera I. Allen;Zhandong Liu
马尔可夫随机场或无向图模型被广泛用于高维多变量数据建模。这些模型的经典实例，如高斯图形模型和伊辛模型，以及最近对单变量指数族指定的图形模型的扩展(Yang等，2012)，都假设所有变量都来自相同的分布。例如，来自高通量基因组学和社交网络的复杂数据通常包含在同一组样本上测量的离散变量、计数变量和连续变量。为了模拟这种异质数据，我们发展了一类新的混合图形模型，通过指定每个节点条件分布是可能不同的单变量指数族的成员。我们研究了我们的模型的几个实例，并提出了可伸缩的M-估计器来恢复底层网络结构。模拟以及从下一代测序和突变数据中学习混合基因组网络的应用表明了我们方法的多功能性。
Markov Random Fields, or undirected graphical models are widely used to model highdimensional multivariate data. Classical instances of these models, such as Gaussian Graphical and Ising Models, as well as recent extensions (Yang et al., 2012) to graphical models specified by univariate exponential families, assume all variables arise from the same distribution. Complex data from high-throughput genomics and social networking for example, often contain discrete, count, and continuous variables measured on the same set of samples. To model such heterogeneous data, we develop a novel class of mixed graphical models by specifying that each node-conditional distribution is a member of a possibly different univariate exponential family. We study several instances of our model, and propose scalable M -estimators for recovering the underlying network structure. Simulations as well as an application to learning mixed genomic networks from next generation sequencing and mutation data demonstrate the versatility of our methods.