TransGraph (version 1.1.0)

Theta.est: Sparse precision matrix estimation.

Description

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

Usage

Theta.est(S.hat.A, delta.hat, lam2=0.1, Omega.hat0=NULL,
                 n=100, max_iter=10, eps=1e-3, method = "cd")

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

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.

lam2

A float value, a tuning parameter.

Omega.hat0

The initial values of the precision matrix, which can be unspecified.

n

The sample size.

max_iter

Int, maximum number of cycles of the algorithm.

eps

A float value, algorithm termination threshold.

method

The optimization algorithm, which can be selected as "admm" (ADMM algorithm) or "cd" (coordinate descent).

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))
omega.hat = Theta.est(S.hat.A, delta.hat, lam2=0.2)