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##A simplex solver for linear programming problem in (N)SIMULE
simule.linprogSPar <- function(i, Sigma, lambda)
{
# num of p * N
# pTimesN = nrow(Sigma)
# num of p * (N + 1)
# Get parameters
q = ncol(Sigma)
p = ncol(Sigma) - nrow(Sigma)
N = nrow(Sigma) / p
# Generate e_j
e = rep(0, p * N)
for(j in 1:N){
e[i + (j - 1) * p] = 1
}
# linear programming solution
f.obj = rep(1, 2 * q)
con1 = cbind(-Sigma, +Sigma)
b1 = lambda - e
b2 = lambda + e
f.con = rbind(-diag(2 * q), con1, -con1)
f.rhs = c(rep(0, 2 * q), b1, b2)
f.dir = rep("<=", length(f.rhs))
lp.out = lp("min", f.obj, f.con, f.dir, f.rhs)
beta = lp.out$solution[1:q] - lp.out$solution[(q + 1):(2 * q)]
if (lp.out$status == 2) warning("No feasible solution! Try a larger tuning parameter!")
return(beta)
}
##' A constrained l1 minimization approach for estimating multiple Sparse
##' Gaussian or Nonparanormal Graphical Models
##' Estimate multiple, related sparse Gaussian or Nonparanormal graphical
##'
##' models from multiple related datasets using the SIMULE algorithm. Please
##' run demo(simule) to learn the basic functions provided by this package.
##' For further details, please read the original paper: Beilun Wang,
##' Ritambhara Singh, Yanjun Qi (2017) \doi{10.1007/s10994-017-5635-7}.
##'
##' The SIMULE algorithm is a constrained l1 minimization method that can
##' detect both the shared and the task-specific parts of multiple graphs
##' explicitly from data (through jointly estimating multiple sparse Gaussian
##' graphical models or Nonparanormal graphical models). It solves the
##' following equation: \deqn{ \hat{\Omega}^{(1)}_I, \hat{\Omega}^{(2)}_I,
##' \dots, \hat{\Omega}^{(K)}_I, \hat{\Omega}_S =
##' \min\limits_{\Omega^{(i)}_I,\Omega_S}\sum\limits_i ||\Omega^{(i)}_I||_1+
##' \epsilon K||\Omega_S||_1 } Subject to : \deqn{
##' ||\Sigma^{(i)}(\Omega^{(i)}_I + \Omega_S) - I||_{\infty} \le \lambda_{n}, i
##' = 1,\dots,K \nonumber } Please also see the equation (7) in our paper. The
##' \eqn{\lambda_n} is the hyperparameter controlling the sparsity level of the
##' matrices and it is the \code{lambda} in our function. The \eqn{\epsilon} is
##' the hyperparameter controlling the differences between the shared pattern
##' among graphs and the individual part of each graph. It is the
##' \code{epsilon} parameter in our function and the default value is 1. For
##' further details, please see our paper:
##' <http://link.springer.com/article/10.1007/s10994-017-5635-7>.
##'
##' @param X A List of input matrices. They can be data matrices or
##' covariance/correlation matrices. If every matrix in the X is a symmetric
##' matrix, the matrices are assumed to be covariance/correlation matrices.
##' @param lambda A positive number. The hyperparameter controls the sparsity
##' level of the matrices. The \eqn{\lambda_n} in the following section:
##' Details.
##' @param epsilon A positive number. The hyperparameter controls the
##' differences between the shared pattern among graphs and the individual part
##' of each graph. The \eqn{\epsilon} in the following section: Details. If
##' epsilon becomes larger, the generated graphs will be more similar to each
##' other. The default value is 1, which means that we set the same weights to
##' the shared pattern among graphs and the individual part of each graph.
##' @param covType A parameter to decide which Graphical model we choose to
##' estimate from the input data.
##'
##' If covType = "cov", it means that we estimate multiple sparse Gaussian
##' Graphical models. This option assumes that we calculate (when input X
##' represents data directly) or use (when X elements are symmetric
##' representing covariance matrices) the sample covariance matrices as input
##' to the simule algorithm.
##'
##' If covType = "kendall", it means that we estimate multiple nonparanormal
##' Graphical models. This option assumes that we calculate (when input X
##' represents data directly) or use (when X elements are symmetric
##' representing correlation matrices) the kendall's tau correlation matrices
##' as input to the simule algorithm.
##' @param intertwined indicate whether to use intertwined covariance matrix
##' @param parallel A boolean. This parameter decides if the package will use
##' the multithreading architecture or not.
##' @return \item{$graphs}{A list of the estimated inverse
##' covariance/correlation matrices.} \item{$share}{The shared graph among
##' multiple tasks.}
##' @author Beilun Wang
##' @references Beilun Wang, Ritambhara Singh, Yanjun Qi (2017). A constrained
##' L1 minimization approach for estimating multiple Sparse Gaussian or
##' Nonparanormal Graphical Models.
##' http://link.springer.com/article/10.1007/s10994-017-5635-7
##' @export
##' @import lpSolve
##' @import parallel
##' @import pcaPP
##' @details if labels are provided in the datalist as column names, result will contain labels (to be plotted)
##' @examples
##' library(JointNets)
##' data(exampleData)
##' result = simule(X = exampleData , lambda = 0.1, epsilon = 0.45, covType = "cov", FALSE)
##' plot(result)
simule <- function(X, lambda, epsilon = 1, covType = "cov", intertwined = FALSE, parallel = FALSE)
{
N = length(X)
for (i in 1:N){
X[[i]] = compute_cov(X[[i]],covType)
}
if (intertwined){
X = intertwined(X,covType = covType)
}
# initialize the parameters
Graphs = list()
p = ncol(X[[1]])
xt = matrix(0, (N + 1) * p, p)
I = diag(1, p, p)
Z = matrix(0, p, p)
# generate the condition matrix A
A = X[[1]]
for(i in 2:N){
A = cbind(A,Z)
}
A = cbind(A,(1/(epsilon * N))*X[[1]])
for(i in 2:N){
temp = Z
for(j in 2:N){
if (j == i){
temp = cbind(temp,X[[i]])
}
else{
temp = cbind(temp,Z)
}
}
temp = cbind(temp, 1/(epsilon * N) * X[[i]])
A = rbind(A, temp)
}
# define the function f for parallelization
f = function(x) simule.linprogSPar(x, A, lambda)
if(parallel == TRUE){ # parallel version
# number of cores to collect,
# default number is number cores in your machine - 1,
# you can set your own number by changing this line.
no_cores = detectCores() - 1
cl = makeCluster(no_cores)
# declare variable and function names to the cluster
clusterExport(cl, list("f", "A", "lambda", "simule.linprogSPar", "lp"), envir = environment())
result = parLapply(cl, 1:p, f)
#print('Done!')
for (i in 1:p){
xt[,i] = result[[i]]
}
stopCluster(cl)
}else{ # single machine code
for (i in 1 : p){
xt[,i] = f(i)
if (i %% 10 == 0){
cat("=")
if(i %% 100 == 0){
cat("+")
}
}
}
#print("Done!")
}
for(i in 1:N){
# combine the results from each column. (\hat{\Omega}_{tot}^1)
Graphs[[i]] = xt[(1 + (i-1) * p):(i * p),] + 1/(epsilon * N) * xt[(1 + N * p):((N + 1) * p),]
# make it be symmetric
for(j in 1:p){
for(k in j:p){
if (abs(Graphs[[i]][j,k]) < abs(Graphs[[i]][k,j])){
Graphs[[i]][j,k] = Graphs[[i]][j,k]
Graphs[[i]][k,j] = Graphs[[i]][j,k]
}
else{
Graphs[[i]][j,k] = Graphs[[i]][k,j]
Graphs[[i]][k,j] = Graphs[[i]][k,j]
}
}
}
}
share = 1/(epsilon * N) * xt[(1 + N * p):((N + 1) * p),]
for(j in 1:p){
for(k in j:p){
if (abs(share[j,k]) < abs(share[k,j])){
share[j,k] = share[j,k]
share[k,j] = share[j,k]
}
else{
share[j,k] = share[k,j]
share[k,j] = share[k,j]
}
}
}
out = list(graphs = Graphs, share = share)
# add names / lables to output precision matrix
class(out) = "simule"
out = add_name_to_out(out,X)
return(out)
}
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