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Graphical Models via Generalized Linear Models (2012)
Eunho Yang
,
Pradeep Ravikumar
, Genevera Allen, and Zhandong Liu
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 ļ¬tting 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.
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PDF
Citation:
NIPS
(2012).
Bibtex:
@inproceedings{YRAL12, title={Graphical Models via Generalized Linear Models}, author={Eunho Yang and Pradeep Ravikumar and Genevera Allen and Zhandong Liu}, booktitle={Advances in Neural Information Processing Systems (NIPS)}, journal={NIPS}, url="http://www.cs.utexas.edu/users/ai-lab/?YRAL12", year={2012} }
People
Pradeep Ravikumar
Faculty
pradeepr [at] cs utexas edu
Eunho Yang
Ph.D. Student
eunho [at] cs utexas edu
Areas of Interest
Graphical Models
High-dimensional Models
Machine Learning
Statistical Learning
Labs
Statistical Learning