Sparse Nonparametric Graphical Models

作     者：Lafferty, John Liu, Han Wasserman, Larry 

作者机构：Univ Chicago Dept Stat Chicago IL 60637 USA Univ Chicago Dept Comp Sci Chicago IL 60637 USA Princeton Univ Dept Operat Res & Financial Engn Princeton NJ 08544 USA Carnegie Mellon Univ Dept Stat Pittsburgh PA 15213 USA Carnegie Mellon Univ Machine Learning Dept Pittsburgh PA 15213 USA 

出 版 物：《STATISTICAL SCIENCE》 (统计科学)

年 卷 期：2012年第27卷第4期

页      面：519-537页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 

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

摘      要：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.