Open Access
November 2012 Sparse Nonparametric Graphical Models
John Lafferty, Han Liu, Larry Wasserman
Statist. Sci. 27(4): 519-537 (November 2012). DOI: 10.1214/12-STS391


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.


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John Lafferty. Han Liu. Larry Wasserman. "Sparse Nonparametric Graphical Models." Statist. Sci. 27 (4) 519 - 537, November 2012.


Published: November 2012
First available in Project Euclid: 21 December 2012

zbMATH: 1331.62219
MathSciNet: MR3025132
Digital Object Identifier: 10.1214/12-STS391

Keywords: consistency , Gaussian copula , high-dimensional inference , kernel density estimation , Oracle inequality , undirected graphical model

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.27 • No. 4 • November 2012
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