Learning additive exponential family graphical models via l2,1-norm regularized M-estimation

Xiao Tong Yuan, Ping Li, Tong Zhang, Qingshan Liu, Guangcan Liu

Research output: Contribution to journalConference articlepeer-review

3 Scopus citations


We investigate a subclass of exponential family graphical models of which the sufficient statistics are defined by arbitrary additive forms. We propose two l2 1-norm regularized maximum likelihood estimators to learn the model parameters from ii.d. samples. The first one is a joint MLE estimator which estimates all the parameters simultaneously. The second one is a node-wise conditional MLE estimator which estimates the parameters for each node individually. For both estimators, statistical analysis shows that under mild conditions the extra flexibility gained by the additive exponential family models comes at almost no cost of statistical efficiency. A Monte-Carlo approximation method is developed to efficiently optimize the proposed estimators. The advantages of our estimators over Gaussian graphical models and Nonparanormal estimators are demonstrated on synthetic and real data sets.

Original languageEnglish (US)
Pages (from-to)4374-4382
Number of pages9
JournalAdvances in Neural Information Processing Systems
StatePublished - 2016
Event30th Annual Conference on Neural Information Processing Systems, NIPS 2016 - Barcelona, Spain
Duration: Dec 5 2016Dec 10 2016

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


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