Statistical Science

Sparse Nonparametric Graphical Models

John Lafferty, Han Liu, and Larry Wasserman

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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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Statist. Sci., Volume 27, Number 4 (2012), 519-537.

First available in Project Euclid: 21 December 2012

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Kernel density estimation Gaussian copula high-dimensional inference undirected graphical model oracle inequality consistency


Lafferty, John; Liu, Han; Wasserman, Larry. Sparse Nonparametric Graphical Models. Statist. Sci. 27 (2012), no. 4, 519--537. doi:10.1214/12-STS391.

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