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Citation

• Vector-Space Markov Random Fields via Exponential Families (pdf, arXiv, software)
  W. Tansey, O. Padilla, A. Suggala, P. Ravikumar.
  In International Conference on Machine Learning (ICML), pp. 684-692, July 2015.
  
  Bibtex:
  
  @inproceedings{tansey2015vectorspa, author = "Wesley Tansey AND Oscar Hernan Madrid Padilla AND Arun Sai Suggala AND Pradeep Ravikumar", title = "Vector-Space Markov Random Fields via Exponential Families", booktitle = "International Conference on Machine Learning (ICML)", page = "684–692", year = "2015", month = "jul", 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." }