Vector-Space Markov Random Fields via Exponential Families

Wesley Tansey, Oscar Hernan Madrid Padilla, Arun Sai Suggala, Pradeep Ravikumar
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:684-692, 2015.

Abstract

We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter exponential family and mixed graphical models, thereby greatly broadening the class of exponential families available (e.g., allowing multinomial and Dirichlet distributions). Specifically, VS-MRFs are the joint graphical model distributions where the node-conditional distributions belong to generic exponential families with general vector space domains. We also present a sparsistent M-estimator for learning our class of MRFs that recovers the correct set of edges with high probability. We validate our approach via a set of synthetic data experiments as well as a real-world case study of over four million foods from the popular diet tracking app MyFitnessPal. Our results demonstrate that our algorithm performs well empirically and that VS-MRFs are capable of capturing and highlighting interesting structure in complex, real-world data. All code for our algorithm is open source and publicly available.

Cite this Paper

BibTeX
@InProceedings{pmlr-v37-tansey15, title = {Vector-Space Markov Random Fields via Exponential Families}, author = {Tansey, Wesley and Padilla, Oscar Hernan Madrid and Suggala, Arun Sai and Ravikumar, Pradeep}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {684--692}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/tansey15.pdf}, url = {https://proceedings.mlr.press/v37/tansey15.html}, abstract = {We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter exponential family and mixed graphical models, thereby greatly broadening the class of exponential families available (e.g., allowing multinomial and Dirichlet distributions). Specifically, VS-MRFs are the joint graphical model distributions where the node-conditional distributions belong to generic exponential families with general vector space domains. We also present a sparsistent M-estimator for learning our class of MRFs that recovers the correct set of edges with high probability. We validate our approach via a set of synthetic data experiments as well as a real-world case study of over four million foods from the popular diet tracking app MyFitnessPal. Our results demonstrate that our algorithm performs well empirically and that VS-MRFs are capable of capturing and highlighting interesting structure in complex, real-world data. All code for our algorithm is open source and publicly available.} }
Endnote
%0 Conference Paper %T Vector-Space Markov Random Fields via Exponential Families %A Wesley Tansey %A Oscar Hernan Madrid Padilla %A Arun Sai Suggala %A Pradeep Ravikumar %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-tansey15 %I PMLR %P 684--692 %U https://proceedings.mlr.press/v37/tansey15.html %V 37 %X We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter exponential family and mixed graphical models, thereby greatly broadening the class of exponential families available (e.g., allowing multinomial and Dirichlet distributions). Specifically, VS-MRFs are the joint graphical model distributions where the node-conditional distributions belong to generic exponential families with general vector space domains. We also present a sparsistent M-estimator for learning our class of MRFs that recovers the correct set of edges with high probability. We validate our approach via a set of synthetic data experiments as well as a real-world case study of over four million foods from the popular diet tracking app MyFitnessPal. Our results demonstrate that our algorithm performs well empirically and that VS-MRFs are capable of capturing and highlighting interesting structure in complex, real-world data. All code for our algorithm is open source and publicly available.
RIS
TY - CPAPER TI - Vector-Space Markov Random Fields via Exponential Families AU - Wesley Tansey AU - Oscar Hernan Madrid Padilla AU - Arun Sai Suggala AU - Pradeep Ravikumar BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-tansey15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 684 EP - 692 L1 - http://proceedings.mlr.press/v37/tansey15.pdf UR - https://proceedings.mlr.press/v37/tansey15.html AB - We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter exponential family and mixed graphical models, thereby greatly broadening the class of exponential families available (e.g., allowing multinomial and Dirichlet distributions). Specifically, VS-MRFs are the joint graphical model distributions where the node-conditional distributions belong to generic exponential families with general vector space domains. We also present a sparsistent M-estimator for learning our class of MRFs that recovers the correct set of edges with high probability. We validate our approach via a set of synthetic data experiments as well as a real-world case study of over four million foods from the popular diet tracking app MyFitnessPal. Our results demonstrate that our algorithm performs well empirically and that VS-MRFs are capable of capturing and highlighting interesting structure in complex, real-world data. All code for our algorithm is open source and publicly available. ER -
APA
Tansey, W., Padilla, O.H.M., Suggala, A.S. & Ravikumar, P.. (2015). Vector-Space Markov Random Fields via Exponential Families. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:684-692 Available from https://proceedings.mlr.press/v37/tansey15.html.

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