# R/GGMPF.R In HeteroGGM: Gaussian Graphical Model-Based Heterogeneity Analysis

#### Documented in GGMPF

```#' GGM-based heterogeneity analysis.
#'
#' @author Mingyang Ren, Sanguo Zhang, Qingzhao Zhang, Shuangge Ma. Maintainer: Mingyang Ren <renmingyang17@mails.ucas.ac.cn>.
#' @references Ren, M., Zhang S., Zhang Q. and Ma S. (2020). Gaussian Graphical Model-based Heterogeneity Analysis via Penalized Fusion. Biometrics, Published Online, https://doi.org/10.1111/biom.13426.
#' @usage GGMPF(lambda, data, K, initial.selection="K-means",
#'              initialize, average=FALSE, asymmetric=TRUE,
#'              eps = 5e-2, maxiter=10, maxiter.AMA=5, local_appro=TRUE,
#'              trace = FALSE, penalty = "MCP", theta.fusion=TRUE)
#'
#' @description The main function of Gaussian graphical model-based heterogeneity analysis via penalized fusion.
#' @param lambda A list, the sequences of the tuning parameters (lambda1, lambda2, and lambda3).
#' @param data n * p matrix, the design matrix.
#' @param K Int, a selected upper bound of K_0.
#' @param initial.selection The different initial values from two clustering methods, which can be selected from c("K-means","dbscan").
#' @param initialize A given initial values, which should be given when initial.selection is not in c("K-means","dbscan").
#' @param average The logical variable, whether to use averaging when integrating parameters that are identified as identical subgroups, the default setting is F, which means the estimated parameters for the subgroup with the largest sample size among the subgroups identified as identical subgroups is used as the final parameter for this subgroup.
#' @param asymmetric The logical variable, symmetry of the precision matrices or not, the default setting is T.
#' @param eps A float value, algorithm termination threshold.
#' @param maxiter Int, maximum number of cycles of the ADMM algorithm.
#' @param maxiter.AMA Int, maximum number of cycles of the AMA algorithm.
#' @param local_appro The logical variable, whether to use local approximations when updating mean parameters, the default setting is T.
#' @param trace The logical variable, whether or not to output the number of identified subgroups during the search for parameters.
#' @param penalty The type of the penalty, which can be selected from c("MCP", "SCAD", "lasso").
#' @param theta.fusion Whether or not the fusion penalty term contains elements of the precision matrices. The default setting is T.
#'
#' @return A list including all estimated parameters and the BIC values with all choices of given tuning parameters, and the selected optional parameters.
#' @export
#' @importFrom stats cov cutree dist hclust kmeans median
#' @importFrom utils combn
#'
#'
GGMPF <- function(lambda, data, K, initial.selection="K-means",
initialize, average=FALSE, asymmetric=TRUE, eps = 5e-2, maxiter=10, maxiter.AMA=5,
local_appro=TRUE, trace = FALSE, penalty = "MCP", theta.fusion=TRUE){

## ------------------------------------------------------------------------------------------------------------------------------------------
## The name of the function: GGMPF
## ------------------------------------------------------------------------------------------------------------------------------------------
## Description:
##            Searching and selecting the optional tuning parameters under the adaptive BIC-type criterion
##            using the proposed method.
## ------------------------------------------------------------------------------------------------------------------------------------------
## Required preceding functions or packages:
##            R functions: FGGM.refit()
## ------------------------------------------------------------------------------------------------------------------------------------------
## Input:
## @ lambda: a list, the sequences of the tuning parameters (lambda1, lambda2, and lambda3).
## @ data: n * p matrix, the design matrix.
## @ K: int, a selected upper bound of K_0.
## @ initial.selection: the different initial values from two clustering methods, which can be selected from c("K-means","dbscan").
## @ initialize: A given initial values, which should be given when initial.selection is not in c("K-means","dbscan").
## @ average: the logical variable, whether to use averaging when integrating parameters that are identified as identical subgroups,
## @          the default setting is F, which means the estimated parameters for the subgroup with the largest sample size among
## @          the subgroups identified as identical subgroups is used as the final parameter for this subgroup.
## @ asymmetric: the logical variable, symmetry of the precision matrices or not, the default setting is T.
## @ eps: a float value, algorithm termination threshold.
## @ maxiter: int, Maximum number of cycles of the ADMM algorithm.
## @ maxiter.AMA: int, Maximum number of cycles of the AMA algorithm.
## @ local_appro: the logical variable, whether to use local approximations when updating mean parameters, the default setting is T.
## @ trace: the logical variable, whether or not to output the number of identified subgroups during the search for parameters.
## ------------------------------------------------------------------------------------------------------------------------------------------
## Output:
## A list "result" including:
## @ Opt_lambda: the selected optional tuning parameters.
## @ Mu_hat.list: the estimated mean vectors of K0_hat subgroups corresponding all choices of given tuning parameters.
## @ Theta_hat.list: the estimated precision matrices of K0_hat subgroups corresponding all choices of given tuning parameters.
## @ prob.list: the estimated mixture probabilities of subgroups corresponding all choices of given tuning parameters.
## @ member.list: subgroup labels to which each sample belongs corresponding all choices of given tuning parameters.
## @ L.mat.list: the estimated probability that each sample belongs to each subgroup corresponding all choices of given tuning parameters.
## @ Opt_aBIC: the optional BIC value.
## @ Opt_num: the position of the optimal parameter for all given parameters.
## ------------------------------------------------------------------------------------------------------------------------------------------

lambda1 = lambda\$lambda1
lambda2 = lambda\$lambda2
lambda3 = lambda\$lambda3
L1 = length(lambda1)
L2 = length(lambda2)
L3 = length(lambda3)
L = L1+L2+L3

aBIC = rep(0,L)
n_all = dim(data)[1]
# initialize
if(initial.selection=="K-means"){
out.initial = initialize_fuc(data,K)
memb = out.initial\$memb
L.mat = matrix(0,n_all,K)
for(jj in 1:n_all) L.mat[jj, memb[jj]]=1
out.initial\$L.mat = L.mat
} else if(initial.selection=="dbscan"){
out.initial = initialize_fuc.dbscan(data,K)
memb = out.initial\$memb
L.mat = matrix(0,n_all,K)
for(jj in 1:n_all) L.mat[jj, memb[jj]]=1
out.initial\$L.mat = L.mat
}
else {out.initial = initialize}

if(L == 3){
l=1
aBIC = rep(0,l)
Mu_hat.list = list()
Theta_hat.list = list()
prob.list = list()
L.mat.list = list()
member.list = list()
lam1 = lambda1;lam2 = lambda2;lam3 = lambda3;
PP = FGGM.refit(data, K, lam1, lam2, lam3, initialization=FALSE, initialize=out.initial, average=average,
asymmetric=asymmetric, local_appro=local_appro, penalty = penalty, theta.fusion=theta.fusion)
mu_hat=PP\$mu;Theta_hat=PP\$Xi;L.mat = PP\$L.mat0;group = PP\$group;prob = PP\$prob0;aBIC[l] = PP\$bic; member = PP\$member
Mu_hat.list[[l]]=mu_hat; Theta_hat.list[[l]]=Theta_hat; prob.list[[l]]=prob; L.mat.list[[l]] = L.mat; member.list[[l]]=member
} else {
Mu_hat.list = list()
Theta_hat.list = list()
prob.list = list()
L.mat.list = list()
member.list = list()
# search lam3
lam1 = median(lambda1);lam2 = median(lambda2)
for (l in 1:L3) {
lam3 = lambda3[l]
PP = FGGM.refit(data, K, lam1, lam2, lam3, initialization=FALSE, initialize=out.initial, average=average,
asymmetric=asymmetric, local_appro=local_appro, penalty = penalty, theta.fusion=theta.fusion)
mu_hat=PP\$mu;Theta_hat=PP\$Xi;L.mat = PP\$L.mat0;group = PP\$group;prob = PP\$prob0;aBIC[l] = PP\$bic; member = PP\$member
Mu_hat.list[[l]]=mu_hat; Theta_hat.list[[l]]=Theta_hat; prob.list[[l]]=prob; L.mat.list[[l]] = L.mat; member.list[[l]]=member
if(trace){
print(c(cat(paste(l,"lam1 lam2 lam3 ="),c(round(lam1,2),round(lam2,2),round(lam3,2)),":"),paste("K =",as.numeric(dim(Theta_hat)[3]))))
}
}
aBIC[is.na(aBIC)] = 10^10
aBIC[aBIC==0] = abs(aBIC[aBIC!=0][1])*10
n_lam3 = which(aBIC[1:L3] == min(aBIC[1:L3]))[1];lam3 = lambda3[n_lam3]

# search lam2
for (l2 in 1:L2) {
lam2 = lambda2[l2];l = L3+l2
PP = FGGM.refit(data, K, lam1, lam2, lam3, initialization=FALSE, initialize=out.initial, average=average,
asymmetric=asymmetric, local_appro=local_appro, penalty = penalty, theta.fusion=theta.fusion)
mu_hat=PP\$mu;Theta_hat=PP\$Xi;L.mat = PP\$L.mat0;group = PP\$group;prob = PP\$prob0;aBIC[l] = PP\$bic; member = PP\$member
Mu_hat.list[[l]]=mu_hat; Theta_hat.list[[l]]=Theta_hat; prob.list[[l]]=prob; L.mat.list[[l]] = L.mat; member.list[[l]]=member
if(trace){
print(c(cat(paste(l,"lam1 lam2 lam3 ="),c(round(lam1,2),round(lam2,2),round(lam3,2)),":"),paste("K =",as.numeric(dim(Theta_hat)[3]))))
}
}
aBIC[is.na(aBIC)] = 10^10
n_lam2 = which(aBIC[(L3+1):(L3+L2)] == min(aBIC[(L3+1):(L3+L2)]))[1];lam2 = lambda2[n_lam2]
# search lam1
for (l1 in 1:L1) {
lam1 = lambda1[l1];l = L3+L2+l1
PP = FGGM.refit(data, K, lam1, lam2, lam3, initialization=F, initialize=out.initial, average=average,
asymmetric=asymmetric, local_appro=local_appro, penalty = penalty, theta.fusion=theta.fusion)
mu_hat=PP\$mu;Theta_hat=PP\$Xi;L.mat = PP\$L.mat0;group = PP\$group;prob = PP\$prob0;aBIC[l] = PP\$bic; member = PP\$member
Mu_hat.list[[l]]=mu_hat; Theta_hat.list[[l]]=Theta_hat; prob.list[[l]]=prob; L.mat.list[[l]] = L.mat; member.list[[l]]=member
if(trace){
print(c(cat(paste(l,"lam1 lam2 lam3 ="),c(round(lam1,2),round(lam2,2),round(lam3,2)),":"),paste("K =",as.numeric(dim(Theta_hat)[3]))))
}
}
aBIC[is.na(aBIC)] = 10^10
aBIC[aBIC==0] = abs(aBIC[aBIC!=0][1])*10
n_lam1 = which(aBIC[(L3+L2+1):(L3+L2+L1)] == min(aBIC[(L3+L2+1):(L3+L2+L1)]))[1];lam1 = lambda1[n_lam1]
}
K.list <- rep(1,length(Theta_hat.list))
for (l in 1:length(Theta_hat.list)) {
K.list[l] <- as.numeric(dim(Theta_hat.list[[l]])[3])
}
aBIC[which(K.list == 1)] <- 10^10

n_lam = which(aBIC == min(aBIC))[1]
Opt_aBIC = min(aBIC)
Opt_lambda = c(lam1,lam2,lam3)
result = list(Opt_lambda=Opt_lambda,Mu_hat.list=Mu_hat.list,Theta_hat.list=Theta_hat.list,prob.list=prob.list,member.list=member.list,L.mat.list=L.mat.list,Opt_aBIC=Opt_aBIC,BIC=aBIC,Opt_num=n_lam)
return(result)
}
```

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HeteroGGM documentation built on Feb. 11, 2021, 5:09 p.m.