# De-Sparsified Graphical Lasso Estimator Compute the de-sparsified (sometimes called "de-biased") glasso estimator with the approach described in Equation 7 of if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="jankova2015confidence;textual",package="GGMncv",cached_env=.Rdpack.currefs) . The basic idea is to **undo** -regularization, in order to compute **p**-values and confidence intervals (i.e., to make statistical inference). ```r desparsify(object, ...) ``` ## Arguments - `object`: An object of class `ggmncv`. - `...`: Currently ignored. ## Returns The de-sparsified estimates, including * `Theta`: De-sparsified precision matrix * `P`: De-sparsified partial correlation matrix ## Details According to if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="jankova2015confidence;textual",package="GGMncv",cached_env=.Rdpack.currefs) , the de-sparisifed estimator, , is defined as where denotes the graphical lasso estimator of the precision matrix and is the sample correlation matrix. Further details can be found in Section 2 ("Main Results") of if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="jankova2015confidence;textual",package="GGMncv",cached_env=.Rdpack.currefs) . This approach is built upon earlier work on the de-sparsified lasso estimator if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="javanmard2014confidence,van2014asymptotically,zhang2014confidence",package="GGMncv",cached_env=.Rdpack.currefs) ## Note This assumes (reasonably) Gaussian data, and should not to be expected to work for, say, polychoric correlations. Further, all work to date has only looked at the graphical lasso estimator, and not de-sparsifying nonconvex regularization. Accordingly, it is probably best to set `penalty = "lasso"` in `ggmncv`. This function only provides the de-sparsified estimator and not **p**-values or confidence intervals (see `inference`). ## Examples ```r # data Y <- GGMncv::Sachs[,1:5] n <- nrow(Y) p <- ncol(Y) # fit model # note: fix lambda, as in the reference fit <- ggmncv(cor(Y), n = nrow(Y), progress = FALSE, penalty = "lasso", lambda = sqrt(log(p)/n)) # fit model # note: no regularization fit_non_reg <- ggmncv(cor(Y), n = nrow(Y), progress = FALSE, penalty = "lasso", lambda = 0) # remove (some) bias and sparsity That <- desparsify(fit) # graphical lasso estimator fit$P # de-sparsified estimator That$P # mle fit_non_reg$P ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs)

desparsify function