TransGraph (version 1.1.0)

Theta.tuning: Sparse precision matrix estimation with tuning parameters.

Description

The fast sparse precision matrix estimation in step 2(b).

Usage

Theta.tuning(lambda2, S.hat.A, delta.hat, Omega.hat0, n.A,
                    theta.algm="cd", adjust.BIC=FALSE)

Value

A result list including:

Theta.hat.m

The optimal precision matrix.

BIC.summary

The summary of BICs.

Theta.hat.list.m

The precision matrices corresponding to a sequence of tuning parameters.

Arguments

lambda2

A vector, a sequence of tuning parameters.

S.hat.A

The sample covariance matrix.

delta.hat

The divergence matrix estimated in step 2(a). If the precision matrix is estimated in the common case (Liu and Luo, 2015, JMVA), it can be set to zero matrix.

Omega.hat0

The initial values of the precision matrix.

n.A

The sample size.

theta.algm

The optimization algorithm used to solve \(\widehat{\Omega}\) in step 2(b), which can be selected as "admm" (ADMM algorithm) or "cd" (coordinate descent).

adjust.BIC

Whether to use the adjusted BIC to select lambda2, the default setting is F.

Author

Mingyang Ren .

References

Ren, M., Zhen Y., and Wang J. (2022). Transfer learning for tensor graphical models. Liu, W. and Luo X. (2015). Fast and adaptive sparse precision matrix estimation in high dimensions, Journal of Multivariate Analysis.

Examples

p = 20
n = 200
omega = diag(rep(1,p))
for (i in 1:p) {
  for (j in 1:p) {
    omega[i,j] = 0.3^(abs(i-j))*(abs(i-j) < 2)
  }
}
Sigma = solve(omega)
X = MASS::mvrnorm(n, rep(0,p), Sigma)
S.hat.A = cov(X)
delta.hat = diag(rep(1,p)) - diag(rep(1,p))
lambda2 = seq(0.1,0.5,length.out =10)
res = Theta.tuning(lambda2, S.hat.A, delta.hat, n.A=n)
omega.hat = res$Theta.hat.m