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Sparse Nonparametric Graphical Models

Author(s): Lafferty, John; Liu, Han; Wasserman, Larry

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Abstract: 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.
Publication Date: 2012
Citation: Lafferty, John, Han Liu, and Larry Wasserman. "Sparse nonparametric graphical models." Statistical Science 27, no. 4 (2012): 519-537. doi:10.1214/12-STS391
DOI: doi:10.1214/12-STS391
ISSN: 0883-4237
EISSN: 2168-8745
Pages: 519 - 537
Type of Material: Journal Article
Journal/Proceeding Title: Statistical Science
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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