Graphical Models via Univariate Exponential Family Distributions

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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.
Publisher
MICROTOME PUBL
Issue Date
2015-12
Language
English
Article Type
Article
Keywords

RNA-SEQ; LASSO; SELECTION; EXPRESSION

Citation

JOURNAL OF MACHINE LEARNING RESEARCH, v.16, pp.3813 - 3847

ISSN
1532-4435
URI
http://hdl.handle.net/10203/212352
Appears in Collection
AI-Journal Papers(저널논문)
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