The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs

TL;DR

This paper introduces a semiparametric approach called the nonparanormal for estimating high-dimensional undirected graphs, relaxing the normality assumption and allowing flexible transformations of variables.

Contribution

It develops a new estimation method for the nonparanormal model, extending Gaussian graphical models with smooth transformations, and analyzes its theoretical properties.

Findings

The nonparanormal method performs well in various examples.

It generalizes Gaussian graphical models to a broader class of distributions.

Theoretical analysis supports its consistency and effectiveness.

Abstract

Recent methods for estimating sparse undirected graphs for real-valued data in high dimensional problems rely heavily on the assumption of normality. We show how to use a semiparametric Gaussian copula--or "nonparanormal"--for high dimensional inference. Just as additive models extend linear models by replacing linear functions with a set of one-dimensional smooth functions, the nonparanormal extends the normal by transforming the variables by smooth functions. We derive a method for estimating the nonparanormal, study the method's theoretical properties, and show that it works well in many examples.