Sparse Nonparametric Graphical Models

TL;DR

This paper explores nonparametric methods for graphical modeling, extending beyond Gaussian assumptions to handle discrete and continuous data more flexibly, with practical examples and future research directions.

Contribution

It introduces two novel nonparametric approaches for graphical models, one extending Gaussian models and another using kernel density estimation for trees and forests.

Findings

Demonstrates nonparametric graphical models for discrete data.

Proposes kernel-based methods for continuous data.

Provides practical examples and discusses future research avenues.

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.