Linearized Bregman solver for composite conditionally likelihood of Gaussian Graphical model with lasso penalty.
Description
Solver for the entire solution path of coefficients.
Usage
1 2 
Arguments
X 
An nbyp matrix of variables. 
kappa 
The damping factor of the Linearized Bregman Algorithm that is defined in the reference paper. See details. 
alpha 
Parameter in Linearized Bregman algorithm which controls the steplength of the discretized solver for the Bregman Inverse Scale Space. See details. 
S 
The covariance matrix can be provided directly if data matrix X is missing. 
c 
Normalized steplength. If alpha is missing, alpha is automatically generated by

tlist 
Parameters t along the path. 
nt 
Number of t. Used only if tlist is missing. Default is 100. 
trate 
tmax/tmin. Used only if tlist is missing. Default is 100. 
print 
If TRUE, the percentage of finished computation is printed. 
Details
The data matrix X is assumed to follow the Gaussian Graohical model which is described as following:
X \sim N(μ, Θ^{1})
where Θ is sparse pbyp symmetric matrix. Then conditional on x_{j}
x_j \sim N(μ_j  ∑_{k\neq j}Θ_{jk}/Θ_{jj}(x_kμ_k),1/Θ_{jj})
then the composite conditional likelihood is like this:
 ∑_{j} condloglik(X_j  X_{j})
or in detail:
∑_{j} Θ_{j}^TSΘ_{j}/2Θ_{jj}  ln(Θ_{jj})/2
where S is covariance matrix of data. It is easy to prove that this loss function
is convex.
Value
A "ggm" class object is returned. The list contains the call, the path, value for alpha, kappa, t.
Author(s)
Jiechao Xiong
Examples
1 2 3 4 5 6 7 8 9 