MGGM.path: Solution path of multiple Gaussion graph model

In MGGM: Structural Pursuit Over Multiple Undirected Graphs

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 λ_1, who controls the sparseness of the estimated precision matrices.
Lambda2.vec	A vector containing tuning parameter λ_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

Author(s)

Yunzhang Zhu, Xiaotong Shen, Wei Pan, Yiwen Sun

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)

MGGM documentation built on May 29, 2017, 8:13 p.m.