Sparse covariance estimation (via glasso) shrinking to a "nonzero" constant

I've only been using R on and off for 9 months and started using the glasso
package for sparse covariance estimation. I know the concept is to shrink
some of the elements of the covariance matrix to zero.

However, say I have a dataset that I know has some underlying "baseline"
covariance/correlation (say, a value of 0.3), how can I change or
incorporate that into to the code? Basically instead of "let's restrict some
of these elements are 0 and others have different nonzero values", I'd like
it to be "let's restrict some of these elements are 0.3 and others are
different or higher/lower than this 0.3". Does that make any sense?



Here is the glasso code if it helps:

library(glasso)
glasso

function (s, rho, zero = NULL, thr = 1e-04, maxit = 10000, approx = FALSE,
? ?penalize.diagonal = TRUE, start = c("cold", "warm"), w.init = NULL,
? ?wi.init = NULL, trace = FALSE)
{
? ?n = nrow(s)
? ?BIG = 1e+10
? ?if (!is.matrix(rho) & length(rho) != 1 & length(rho) != nrow(s)) {
? ? ? ?stop("Wrong number of elements in rho")
? ?}
? ?if (length(rho) == 1 & rho == 0) {
? ? ? ?cat("With rho=0, there may be convergence problems if the input
matrix s\n is not of full rank",
? ? ? ? ? ?fill = TRUE)
? ?}
? ?if (is.vector(rho)) {
? ? ? ?rho = matrix(sqrt(rho)) %*% sqrt(rho)
? ?}
? ?if (length(rho) == 1) {
? ? ? ?rho = matrix(rho, ncol = n, nrow = n)
? ?}
? ?if (!is.null(zero)) {
? ? ? ?if (!is.matrix(zero)) {
? ? ? ? ? ?zero = matrix(zero, nrow = TRUE)
? ? ? ?}
? ? ? ?for (k in 1:nrow(zero)) {
? ? ? ? ? ?i = zero[k, 1]
? ? ? ? ? ?j = zero[k, 2]
? ? ? ? ? ?rho[i, j] = BIG
? ? ? ? ? ?rho[j, i] = BIG
? ? ? ?}
? ?}
? ?start.type = match.arg(start)
? ?if (start.type == "cold") {
? ? ? ?is = 0
? ? ? ?ww = xx = matrix(0, nrow = n, ncol = n)
? ?}
? ?if (start.type == "warm") {
? ? ? ?is = 1
? ? ? ?if (is.null(w.init) | is.null(wi.init)) {
? ? ? ? ? ?stop("Warm start specified: w.init and wi.init must be non-null")
? ? ? ?}
? ? ? ?ww = w.init
? ? ? ?xx = wi.init
? ?}
? ?itrace = 1 * trace
? ?ipen = 1 * (penalize.diagonal)
? ?ia = 1 * approx
? ?mode(rho) = "double"
? ?mode(s) = "double"
? ?mode(ww) = "double"
? ?mode(xx) = "double"
? ?mode(n) = "integer"
? ?mode(maxit) = "integer"
? ?mode(ia) = "integer"
? ?mode(itrace) = "integer"
? ?mode(ipen) = "integer"
? ?mode(is) = "integer"
? ?mode(thr) = "double"
? ?junk <- .Fortran("glasso", n, s, rho, ia, is, itrace, ipen,
? ? ? ?thr, maxit = maxit, ww = ww, xx = xx, niter = integer(1),
? ? ? ?del = double(1), ierr = integer(1), PACKAGE = "glasso")
? ?ww = matrix(junk$ww, ncol = n)
? ?xx = matrix(junk$xx, ncol = n)
? ?if (junk$ierr != 0) {
? ? ? ?stop("memory allocation error")
? ?}
? ?critfun = function(Sigmahati, s, rho, penalize.diagonal = TRUE) {
? ? ? ?d = det(Sigmahati)
? ? ? ?temp = Sigmahati
? ? ? ?if (!penalize.diagonal) {
? ? ? ? ? ?diag(temp) = 0
? ? ? ?}
? ? ? ?val = -log(d) + sum(diag(s %*% Sigmahati)) + sum(abs(rho *
? ? ? ? ? ?temp))
? ? ? ?return(val)
? ?}
? ?crit = critfun(xx, s, rho, penalize.diagonal)
? ?return(list(w = ww, wi = xx, loglik = -(n/2) * crit, errflag = junk$ierr,
? ? ? ?approx = approx, del = junk$del, niter = junk$niter))
}



If anyone can give any suggestions, I'd greatly appreciate it. Thanks!




Vivian