The nonparanormal: Semiparametric estimation of high dimensional undirected graphs

Han Liu, John Lafferty, Larry Wasserman

Research output: Contribution to journalArticlepeer-review

303 Scopus citations


Recent methods for estimating sparse undirected graphs for real-valued data in high dimensional problems rely heavily on the assumption of normality. We show how to use a semiparametric Gaussian copula - or "nonparanormal" - for high dimensional inference. Just as additive models extend linear models by replacing linear functions with a set of one-dimensional smooth functions, the nonparanormal extends the normal by transforming the variables by smooth functions. We derive a method for estimating the nonparanormal, study the method's theoretical properties, and show that it works well in many examples.

Original languageAmerican English
Pages (from-to)2295-2328
Number of pages34
JournalJournal of Machine Learning Research
StatePublished - 2009

ASJC Scopus subject areas

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


  • Gaussian copula
  • Graphical lasso
  • Graphical models
  • High dimensional inference
  • Occult
  • Paranormal
  • Sparsity
  • ℓ regularization


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