nips nips2012 nips2012-147 nips2012-147-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Eunho Yang, Genevera Allen, Zhandong Liu, Pradeep K. Ravikumar
Abstract: Undirected graphical models, also known as Markov networks, enjoy popularity in a variety of applications. The popular instances of these models such as Gaussian Markov Random Fields (GMRFs), Ising models, and multinomial discrete models, however do not capture the characteristics of data in many settings. We introduce a new class of graphical models based on generalized linear models (GLMs) by assuming that node-wise conditional distributions arise from exponential families. Our models allow one to estimate multivariate Markov networks given any univariate exponential distribution, such as Poisson, negative binomial, and exponential, by fitting penalized GLMs to select the neighborhood for each node. A major contribution of this paper is the rigorous statistical analysis showing that with high probability, the neighborhood of our graphical models can be recovered exactly. We also provide examples of non-Gaussian high-throughput genomic networks learned via our GLM graphical models. 1
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