Sparse nonparametric graphical models

John Lafferty, Han Liu, Larry Wasserman

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


We present some nonparametric methods for graphical modeling. In the discrete case, where the data are binary or drawn from a finite alphabet, Markov random fields are already essentially nonparametric, since the cliques can take only a finite number of values. Continuous data are different. The Gaussian graphical model is the standard parametric model for continuous data, but it makes distributional assumptions that are often unrealistic. We discuss two approaches to building more flexible graphical models. One allows arbitrary graphs and a nonparametric extension of the Gaussian; the other uses kernel density estimation and restricts the graphs to trees and forests. Examples of both methods are presented. We also discuss possible future research directions for nonparametric graphical modeling.

Original languageEnglish (US)
Pages (from-to)519-537
Number of pages19
JournalStatistical Science
Issue number4
StatePublished - Nov 2012

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


  • Consistency
  • Gaussian copula
  • Highdimensional inference
  • Kernel density estimation
  • Oracle inequality
  • Undirected graphical model


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