The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs
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.
high dimensional inference graphical models gaussian copula sparsity l(1) regularization graphical lasso paranormal occult