The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs

Han Liu, John Lafferty, Larry Wasserman.

Year: 2009, Volume: 10, Issue: 80, Pages: 2295−2328


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.