GGMncv (version 2.1.1)

desparsify: De-Sparsified Graphical Lasso Estimator

Description

Compute the de-sparsified (sometimes called "de-biased") glasso estimator with the approach described in Equation 7 of jankova2015confidence;textualGGMncv. The basic idea is to undo L_1-regularization, in order to compute p-values and confidence intervals (i.e., to make statistical inference).

Usage

desparsify(object, ...)

Arguments

object

An object of class ggmncv.

...

Currently ignored.

Value

The de-sparsified estimates, including

• Theta: De-sparsified precision matrix

• P: De-sparsified partial correlation matrix

Details

According to jankova2015confidence;textualGGMncv, the de-sparisifed estimator, T, is defined as

T = 2 - R,

where denotes the graphical lasso estimator of the precision matrix and R is the sample correlation matrix. Further details can be found in Section 2 ("Main Results") of jankova2015confidence;textualGGMncv.

This approach is built upon earlier work on the de-sparsified lasso estimator javanmard2014confidence,van2014asymptotically,zhang2014confidenceGGMncv

References

Examples

# NOT RUN {
# 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
# }