Graphical Models via Univariate Exponential Family Distributions

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dc.citation.firstpage3813en_US
dc.citation.journalTitleJournal of Machine Learning Researchen_US
dc.citation.lastpage3847en_US
dc.citation.volumeNumber16en_US
dc.contributor.authorYang, Eunhoen_US
dc.contributor.authorRavikumar, Pradeepen_US
dc.contributor.authorAllen, Genevera I.en_US
dc.contributor.authorLiu, Zhandongen_US
dc.date.accessioned2016-10-21T18:32:23Zen_US
dc.date.available2016-10-21T18:32:23Zen_US
dc.date.issued2015en_US
dc.description.abstractUndirected 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.en_US
dc.identifier.citationYang, Eunho, Ravikumar, Pradeep, Allen, Genevera I., et al.. "Graphical Models via Univariate Exponential Family Distributions." <i>Journal of Machine Learning Research,</i> 16, (2015) JMLR: 3813-3847. <a href="https://hdl.handle.net/1911/91985">https://hdl.handle.net/1911/91985</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/91985en_US
dc.language.isoengen_US
dc.publisherJMLRen_US
dc.relation.urihttp://www.jmlr.org/papers/v16/yang15a.htmlen_US
dc.rightsThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by JMLR.en_US
dc.subject.keywordgraphical modelsen_US
dc.subject.keywordmodel selectionen_US
dc.subject.keywordsparse estimationen_US
dc.titleGraphical Models via Univariate Exponential Family Distributionsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpost-printen_US
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