MGGM (version 1.0)

MGGM.path: Solution path of multiple Gaussion graph model

Description

MGGM.path gives the solution paths for both convex and non-convex version of multiple Gaussion graph model(MGGM). See $[1]$ for detail of MGGM.

Usage

MGGM.path(S_bar, nn, Lambda1.vec, Lambda2.vec, graph, tau = 0.01, 
MAX_iter = 200, eps_mat = 1e-04)

Arguments

S_bar

A matrix with dimension $(p, p*L)$. It contains all sample covariance matrices over all $L$ observed stages.

nn

A $L$-length vector, indicating the sample size on each observed stage.

Lambda1.vec

A vector containing tuning parameter $\lambda_1$, who controls the sparseness of the estimated precision matrices.

Lambda2.vec

A vector containing tuning parameter $\lambda_2$, who controls the degree of clustering of the estimated precision matrices.

graph

A matrix with dimension $(2,E)$, where $E$ is the number of edges. Each column of $graph$ indicates an edge by the indices of connected graphs.

tau

The tuning parameter used in truncated $L_1$ penalty(TLP).

MAX_iter

The maximum iteration for DC programming.

eps_mat

The convergence criterion of swiping columns.

Value

sol_nonconvex

An array with dimension $(p,p*L,length(Lambda2.vec),length(Lambda2.vec))$, is the solution path of the non-convex problem, containing all estimated precision matrices over all time and all pairs of tuning parameters.

sol_convex

An array with dimension $(p,p*L,length(Lambda2.vec),length(Lambda2.vec))$, is the solution path of the convex problem, containing all estimated precision matrices over all time and all pairs of tuning parameters.

aa

References

$[1]$ Yunzhang Zhu, Xiaotong Shen, Wei Pan. Structural pursuit over multiple undirected graphs

Examples

library(MASS)

## generating L true sparse precision and covariance matrices
L <- num_of_matrix <- 4 
## two different underlying matrices
L0 <- 2 
p <- dim_of_matrix <-  20
n <- 120 #number of observations for each l
nn <- rep(n,L)
MAX_iter <- 200 #max number of iterations

Gene_cov<-function(p){
    sigma <- runif(p-1,0.5,1)
    covmat0 <- diag(1,p)
    for (i in 1:(p-1)){
        for (j in (i+1):p){
            temp <- exp(-sum(sigma[i:(j-1)]/2))
            covmat0[i,j] <- temp
            covmat0[j,i] <- temp
        }
    }
    return(covmat0)
}
covmat1 <- Gene_cov(p)
covmat_inverse1 <- solve(covmat1)
covmat2 <- Gene_cov(p)
covmat_inverse2 <- solve(covmat2)

## set first L/2 and last L/2 matrices to be the same
covmat0 <- cbind(matrix(rep(covmat1,L/2),p,p*L/2), matrix(rep(covmat2,L/2),p,p*L/2))
covmat_inverse0 <- cbind(matrix(rep(covmat_inverse1,L/2),p,p*L/2),
matrix(rep(covmat_inverse2,L/2),p,p*L/2)) 


## generating sample covariance matrices S_bar = [S_1, ... S_L]
S_bar <- matrix(0,p,L*p) 
for (l in 1:L){
    temp <- mvrnorm(n = nn[l], rep(0,p), covmat0[,((l-1)*p+1):(l*p)])
    S_bar[,((l-1)*p+1):(l*p)] <- crossprod(temp) / nn[l]
}


## matrices generation ends
Lambda1.vec <- log(p)*c(.8, .5, .4, .3, 0.2) #lasso penlaty
Lambda2.vec <- log(p)*c(.1, .08, .06, .05, .04, .03, .0) #grouping penalty
tau <- c(0.01) #thresholding parameter

## generating graphs
graph_complete = matrix(0,2,L*(L-1)/2)
for (l1 in 1:(L-1)){
  graph_complete[,(L*(l1-1)-(l1-1)*l1/2+1):(L*l1-l1*(l1+1)/2)] = rbind(rep(l1,L-l1),(l1+1):L)
}
graph <- graph_complete - 1

sol_path <- MGGM.path(S_bar, nn, Lambda1.vec, Lambda2.vec, graph, tau)