Sparse Nonparametric Graphical Models
This addresses the need for more flexible graphical models in statistical analysis, though it appears incremental as it builds on existing nonparametric and graphical modeling concepts.
The paper tackles the problem of unrealistic distributional assumptions in Gaussian graphical models for continuous data by presenting two nonparametric approaches: one allowing arbitrary graphs with a nonparametric Gaussian extension, and another using kernel density estimation restricted to trees and forests.
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.