On semiparametric exponential family graphical models

Zhuoran Yang, Yang Ning, Han Liu

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We propose a new class of semiparametric exponential family graphical models for the analysis of high dimensional mixed data. Different from the existing mixed graphical models, we allow the nodewise conditional distributions to be semiparametric generalized linear models with unspecified base measure functions. Thus, one advantage of our method is that it is unnecessary to specify the type of each node and the method is more convenient to apply in practice. Under the proposed model, we consider both problems of parameter estimation and hypothesis testing in high dimensions. In particular, we propose a symmetric pairwise score test for the presence of a single edge in the graph. Compared to the existing methods for hypothesis tests, our approach takes into account of the symmetry of the parameters, such that the inferential results are invariant with respect to the different parametrizations of the same edge. Thorough numerical simulations and a real data example are provided to back up our theoretical results.

Original languageEnglish (US)
Pages (from-to)1-59
Number of pages59
JournalJournal of Machine Learning Research
Volume19
StatePublished - Oct 1 2018

Funding

The authors are grateful for the support of NSF CAREER Award DMS1454377, NSF IIS1408910, NSF IIS1332109, NIH R01MH102339, NIH R01GM083084, and NIH R01HG06841.

Keywords

  • Exponential Family
  • Graphical Models
  • High Dimensional Inference

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Statistics and Probability
  • Artificial Intelligence

Fingerprint

Dive into the research topics of 'On semiparametric exponential family graphical models'. Together they form a unique fingerprint.

Cite this