  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.
