Mixed Graphical Models via Exponential Families

Eunho Yang, Yulia Baker, Pradeep Ravikumar, Genevera Allen, Zhandong Liu
Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, PMLR 33:1042-1050, 2014.

Abstract

Markov Random Fields, or undirected graphical models are widely used to model high-dimensional multivariate data. Classical instances of these models, such as Gaussian Graphical and Ising Models, as well as recent extensions to graphical models specified by univariate exponential families, assume all variables arise from the same distribution. Complex data from high-throughput genomics and social networking for example, often contain discrete, count, and continuous variables measured on the same set of samples. To model such heterogeneous data, we develop a \emphnovel class of mixed graphical models by specifying that each node-conditional distribution is a member of a possibly different univariate exponential family. We study several instances of our model, and propose scalable M-estimators for recovering the underlying network structure. Simulations as well as an application to learning mixed genomic networks from next generation sequencing and mutation data demonstrate the versatility of our methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v33-yang14a, title = {{Mixed Graphical Models via Exponential Families}}, author = {Yang, Eunho and Baker, Yulia and Ravikumar, Pradeep and Allen, Genevera and Liu, Zhandong}, booktitle = {Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics}, pages = {1042--1050}, year = {2014}, editor = {Kaski, Samuel and Corander, Jukka}, volume = {33}, series = {Proceedings of Machine Learning Research}, address = {Reykjavik, Iceland}, month = {22--25 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v33/yang14a.pdf}, url = {https://proceedings.mlr.press/v33/yang14a.html}, abstract = {Markov Random Fields, or undirected graphical models are widely used to model high-dimensional multivariate data. Classical instances of these models, such as Gaussian Graphical and Ising Models, as well as recent extensions to graphical models specified by univariate exponential families, assume all variables arise from the same distribution. Complex data from high-throughput genomics and social networking for example, often contain discrete, count, and continuous variables measured on the same set of samples. To model such heterogeneous data, we develop a \emphnovel class of mixed graphical models by specifying that each node-conditional distribution is a member of a possibly different univariate exponential family. We study several instances of our model, and propose scalable M-estimators for recovering the underlying network structure. Simulations as well as an application to learning mixed genomic networks from next generation sequencing and mutation data demonstrate the versatility of our methods.} }
Endnote
%0 Conference Paper %T Mixed Graphical Models via Exponential Families %A Eunho Yang %A Yulia Baker %A Pradeep Ravikumar %A Genevera Allen %A Zhandong Liu %B Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2014 %E Samuel Kaski %E Jukka Corander %F pmlr-v33-yang14a %I PMLR %P 1042--1050 %U https://proceedings.mlr.press/v33/yang14a.html %V 33 %X Markov Random Fields, or undirected graphical models are widely used to model high-dimensional multivariate data. Classical instances of these models, such as Gaussian Graphical and Ising Models, as well as recent extensions to graphical models specified by univariate exponential families, assume all variables arise from the same distribution. Complex data from high-throughput genomics and social networking for example, often contain discrete, count, and continuous variables measured on the same set of samples. To model such heterogeneous data, we develop a \emphnovel class of mixed graphical models by specifying that each node-conditional distribution is a member of a possibly different univariate exponential family. We study several instances of our model, and propose scalable M-estimators for recovering the underlying network structure. Simulations as well as an application to learning mixed genomic networks from next generation sequencing and mutation data demonstrate the versatility of our methods.
RIS
TY - CPAPER TI - Mixed Graphical Models via Exponential Families AU - Eunho Yang AU - Yulia Baker AU - Pradeep Ravikumar AU - Genevera Allen AU - Zhandong Liu BT - Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics DA - 2014/04/02 ED - Samuel Kaski ED - Jukka Corander ID - pmlr-v33-yang14a PB - PMLR DP - Proceedings of Machine Learning Research VL - 33 SP - 1042 EP - 1050 L1 - http://proceedings.mlr.press/v33/yang14a.pdf UR - https://proceedings.mlr.press/v33/yang14a.html AB - Markov Random Fields, or undirected graphical models are widely used to model high-dimensional multivariate data. Classical instances of these models, such as Gaussian Graphical and Ising Models, as well as recent extensions to graphical models specified by univariate exponential families, assume all variables arise from the same distribution. Complex data from high-throughput genomics and social networking for example, often contain discrete, count, and continuous variables measured on the same set of samples. To model such heterogeneous data, we develop a \emphnovel class of mixed graphical models by specifying that each node-conditional distribution is a member of a possibly different univariate exponential family. We study several instances of our model, and propose scalable M-estimators for recovering the underlying network structure. Simulations as well as an application to learning mixed genomic networks from next generation sequencing and mutation data demonstrate the versatility of our methods. ER -
APA
Yang, E., Baker, Y., Ravikumar, P., Allen, G. & Liu, Z.. (2014). Mixed Graphical Models via Exponential Families. Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 33:1042-1050 Available from https://proceedings.mlr.press/v33/yang14a.html.

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