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Graphical Models via Generalized Linear Models
Eunho Yang · Pradeep Ravikumar · Genevera I Allen · zhandong Liu

Wed Dec 05 07:00 PM -- 12:00 AM (PST) @ Harrah’s Special Events Center 2nd Floor #None

Undirected graphical models, or Markov networks, such as Gaussian graphical models and Ising models enjoy popularity in a variety of applications. In many settings, however, data may not follow a Gaussian or binomial distribution assumed by these models. We introduce a new class of graphical models based on generalized linear models (GLM) by assuming that node-wise conditional distributions arise from exponential families. Our models allow one to estimate networks for a wide class of exponential distributions, such as the 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 provide examples of high-throughput genomic networks learned via our GLM graphical models for multinomial and Poisson distributed data.

Author Information

Eunho Yang (IBM Research)
Pradeep Ravikumar (Carnegie Mellon University)
Genevera I Allen (Rice University)
zhandong Liu (University of Pennsylvania)

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