simulation_SmS.R
In dariamed/gjamed: What the package does (short line)
rm(list=ls())
#setwd("~/Bureau/PY_comp0306/gjamed-master")
setwd("~/Documents/GitHub/gjamed")
########## Simulating the data
library(MASS)
library(repmis)
library(gjam)
library(rlist)
library(truncnorm)
#library(coda)
library(RcppArmadillo)
library(arm)
library(NLRoot)
library(Rcpp)
library(plyr)
library(ggplot2)
#library(ggsn)
library(parallel)
Rcpp::sourceCpp('src/cppFns.cpp')
source("R/gjamHfunctions_mod.R")
source("R/simple_gjam_0.R")
source("R/simple_gjam_1.R")
source("R/simple_gjam_2.R")
source("R/simple_gjam_3.R")
source("R/simple_gjam_4.R")
generate_data<-function(Sp=50,nsamples=500,qval=20,Ktrue=4){
S<-Sp
n<- nsamples
q<- qval
env<-runif(-50,50,n=n)
X<-cbind(1,poly(env,2)) #nxK
idx<-sample(S)
B_0<-seq(0,100,length.out=S)[idx]
B_1<-seq(0,100,length.out=S)[idx]
B_2<-seq(0,100,length.out=S)[idx]
B<-cbind(B_0,B_1,B_2) #SxK
L<-X%*%t(B) #nxS
K_t<- Ktrue
cat("True number of clusters : ",K_t,"\n")
A<-matrix(NA,nrow=ceiling(K_t),ncol=q)
for(i in 1:ceiling(K_t)){
A[i,]<-mvrnorm(n = 1,rep(0,q), Sigma=3*diag(q)) #Nxq short and skinny
}
idx<-sample((1:ceiling(K_t)),S,replace=T)
Lambda<-A[idx,] #Sxr tall and skinny
Sigma<-Lambda%*%t(Lambda)+0.1*diag(S) #SxS
Sigma_true<-Sigma
Y<-mvrnorm(n = n, mu=rep(0,S), Sigma=Sigma)
xdata<-as.data.frame(X[,-1])
colnames(xdata)<-c("env1","env2")
return(list(xdata=xdata, Y=Y,idx=idx,S_true=Sigma_true))
}
simulation_fun_oneDS<-function(data_set,Sp, Ntr, rval,nsamples=500, Ktrue,q=20, it=1000, burn=500,type="GJAM"){
S<-Sp
n<- nsamples
r <- rval
iterations<-it
#env<-runif(-50,50,n=n)
#X<-cbind(1,poly(env,2)) #nxK
#idx<-sample(S)
#B_0<-seq(0,100,length.out=S)[idx]
#B_1<-seq(0,100,length.out=S)[idx]
#B_2<-seq(0,100,length.out=S)[idx]
#B<-cbind(B_0,B_1,B_2) #SxK
#L<-X%*%t(B) #nxS
K=sum(S/(S+(1:S)-1)) #104, his prior number of clusters when alpha=S
if(type=="GJAM"){ cat("Prior expected number of clusters : ",K,"\n")}
else{cat("Prior expected number of clusters : ",Ktrue,"\n")}
K_t= Ktrue
cat("True number of clusters : ",K_t,"\n")
xdata<-data_set$xdata
Y<-data_set$Y
idx<- data_set$idx
Sigma_true<- data_set$S_true
formula<-as.formula(~env1+env2)
if(type=="GJAM"){
rl <- list(r = r, N =Ntr-1)
ml<-list(ng=it,burnin=burn,typeNames='CON',reductList=rl)
fit<-gjam(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-NULL
alpha.DP<-S
pk_chains<-NULL
pk<-NULL
alpha.chains_short<-NULL
pN_chain_short<-NULL
}
if(type=="0"){
#func<-function(x) {sum(x/(x+(1:S)-1))-K_t}
#alpha.DP<-.bisec(func,0.01,100)
alpha.DP<-S
rl <- list(r = r, N =Ntr-1,alpha.DP=alpha.DP)
ml<-list(ng=it,burnin=burn,typeNames='CON',reductList=rl)
fit<-.gjam0(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-NULL
alpha.chains_short<-NULL
pk_chains<- fit$chains$pk_g
}
if(type=="1"){
func<-function(x) {sum(x/(x+(1:S)-1))-K_t}
alpha.DP<-.bisec(func,0.01,100)
shape=((alpha.DP)^2)/20
rate=alpha.DP/20
rl <- list(r = r, N = Ntr-1, rate=rate,shape=shape)
ml<-list(ng=it,burnin=burn,typeNames='CON',reductList=rl)
fit<-.gjam_1(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-fit$chains$alpha.DP_g
pk_chains<- fit$chains$pk_g
}
if(type=="2"){
func<-function(x) {sum(x/(x+(1:S)-1))-K_t}
alpha.DP<-.bisec(func,0.01,100)
shape=((alpha.DP)^2)/20
rate=alpha.DP/20
rl <- list(r = r, N = Ntr-1, rate=rate,shape=shape,V=1)
ml<-list(ng=it,burnin=burn,typeNames='CON',reductList=rl)
fit<-.gjam_2(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-fit$chains$alpha.DP_g
pk_chains<- fit$chains$pk_g
}
if(type=="3"){
eps=0.01
sigma_py<-0.25
funcPY_root<-function(x) {(x/sigma_py)*(prod((x+sigma_py+c(1:S) -1)/(x+c(1:S) -1))-1) - K_t}
alpha.PY<-.bisec(funcPY_root,0.0001,100)
N_eps<-floor(.compute_tau_mean(sigma_py,alpha.PY,eps) + 2*.compute_tau_var(sigma_py,alpha.PY,eps))
rl <- list(r = r, N = N_eps, sigma_py=sigma_py, alpha=alpha.PY)
ml<-list(ng=it,burnin=burn,typeNames='CON',reductList=rl)
fit<-.gjam_3(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-NULL
alpha.chains_short<-NULL
pk_chains<- fit$chains$pk_g
alpha.DP<-alpha.PY
Ntr<-N_eps+1
}
if(type=="4"){
eps=0.1
alp_sig<-as.data.frame(matrix(NA,nrow=20,ncol=3))
colnames(alp_sig)<-c("alpha","sigma","is_less_150")
alp_sig$sigma=seq(0.05,0.4,length.out = 20)
#loop to run bisecetion on a grid for sigma
for(i in 1:20){
####corrected added -1
func<-function(x) {(x/alp_sig[i,"sigma"])*(prod((x+alp_sig[i,"sigma"]+c(1:S)-1)/(x+c(1:S) -1))-1) - K_t}
alp_sig[i,"alpha"]<-.bisec(func,0.01,100)
N_eps<-floor(.compute_tau_mean(alp_sig[i,"sigma"], alp_sig[i,"alpha"],eps) + 2*.compute_tau_var(alp_sig[i,"sigma"], alp_sig[i,"alpha"],eps))
ifelse(N_eps<=150,alp_sig[i,"is_less_150"]<-T,alp_sig[i,"is_less_150"]<-F)
N_eps
}
if(sum(alp_sig$is_less_150==T)==0) cat("!! no choice under N=150, need to recheck!!!")
k<-max(which(alp_sig$is_less_150==T)) #max sigma s.t. N<150
sigma_py<-alp_sig[k,"sigma"]
alpha.PY<-alp_sig[k,"alpha"]
#fixing hyperparameters
ro.disc=1-2* sigma_py
shape=((alpha.PY)^2)/10
rate=alpha.PY/10
# 95% quantile of alpha
alpha.max=qgamma(.95, shape=shape, rate=rate)
#alpha.max_val<-5
sigma_py_max<-0.5
N_eps<-floor(.compute_tau_mean_large_dim(sigma_py_max,alpha.max,eps) + 2*.compute_tau_var_large_dim(sigma_py_max,alpha.max,eps))
rl <- list(r = r, N = N_eps,rate=rate,shape=shape,V1=1,ro.disc=ro.disc) #here to modify N
ml<-list(ng=it,burnin=burn,typeNames='CON',reductList=rl)
fit<-.gjam_4(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-fit$chains$alpha.PY_g
sigma.chains<-fit$chains$discount.PY_g
pk_chains<- fit$chains$pk_g
Ntr<-N_eps+1
alpha.DP<-alpha.PY
}
trace<-apply(fit$chains$kgibbs,1,function(x) length(unique(x)))
ind_trace<- seq(1,it,by=5)
trace_short<- trace[ind_trace]
df<-as.data.frame(trace)
df$iter<-1:it
#plot(apply(fit$chains$kgibbs,1,function(x) length(unique(x))))
p<-ggplot(df, aes(y=trace, x=iter)) + geom_point() +
labs(title=paste0("Trace plot for the number of groups K for S=",S," r=",r," true K=",K_t," type=",type), caption=paste0("Number of iterations: ",it," burnin: ",burn,"number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))+
geom_hline(yintercept = Ktrue,color = "red")
#plot(p)
#####Weights plot
if(type%in%c("0","1","2","3","4")){
pk<- apply(fit$chains$pk_g[-c(1:burn),],2,mean)
last_pk<- round(pk[Ntr-1],3)
df_weights <- data.frame(matrix(NA, nrow = Ntr-1, ncol =1))
df_weights$pw<-pk
df_weights$tr<-1:(Ntr-1)
pl_weigths<- ggplot(df_weights, aes(x=tr, y=pw)) +
geom_segment( aes(x=tr,xend=tr,y=0,yend=pw)) +
geom_point( size=0.5, color="red", fill=alpha("blue", 0.3), alpha=0.4, shape=21, stroke=2)+ labs(title=paste0("Weights for the case: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr, " pN=",last_pk), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
# pl_weigths
}
#####Alpha plot
if(type%in%c("1","2","4")){
df_alpha <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
df_alpha$alpha<- alpha.chains[-c(1:burn)]
df_alpha$type<- "posterior"
df_alpha_prior <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
#df_alpha_prior$alpha<- rgamma(it-burn, shape, rate)
alpha_seq= seq(min(alpha.chains[-c(1:burn)]),max(alpha.chains[-c(1:burn)]),length=it-burn)
df_alpha_prior$alpha <- dgamma(alpha_seq,rate,shape)
df_alpha_prior$type<- "prior"
df_alpha_all<- rbind(df_alpha[-1,],df_alpha_prior[-1,])
###Compute mean
mu <- ddply(df_alpha_all, "type", summarise, grp.mean=mean(alpha))
mu$grp.mean[which(mu$type=="prior")]=alpha.DP
p_alpha_1<- ggplot(df_alpha_all, aes(x=alpha, color=type)) + geom_vline(data=mu, aes(xintercept=grp.mean, color=type),linetype="dashed")+
geom_density()+labs(title=paste0("Distribution alpha: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
# p_alpha_1
p_alpha_2<- ggplot(df_alpha, aes(x=alpha)) + geom_vline(data=mu, aes(xintercept=grp.mean, color=type),linetype="dashed")+
geom_density(color="red")+labs(title=paste0("Posterior distribution for alpha"), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples," S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))+
scale_color_manual(name = c("Legend"), values = c("prior"="#9999FF", "posterior"= "#FF6666"), labels=c("posterior mean","prior mean"))
# p_alpha_2
}
#######Sigma plot
if(type%in%c("4")){
df_sigma <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
df_sigma$sigma<- sigma.chains[-c(1:burn)]
###Compute mean
mu <- ddply(df_sigma, type, summarise, grp.mean=mean(sigma))
p_sigma<- ggplot(df_sigma, aes(x=sigma)) + geom_vline(data=mu, aes(xintercept=grp.mean),linetype="dashed")+
geom_density()+labs(title=paste0("Distribution sigma: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
# p_sigma
dfs<-as.data.frame(sigma.chains)
dfs$iter<-1:it
#plot(apply(fit$chains$kgibbs,1,function(x) length(unique(x))))
p_trace_sigma<-ggplot(dfs, aes(y=sigma.chains, x=iter)) + geom_point() +
labs(title=paste0("Trace plot for the sigma for S=",S," r=",r," true K=",K_t," type=",type), caption=paste0("Number of iterations: ",it," burnin: ",burn,"number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
# p_trace_sigma
}
N_dim<-(it-burn)
sigma<-array(dim=c(Sp,Sp,N_dim))
for(j in 1:N_dim){
K<-fit$chains$kgibbs[j,]
Z <- matrix(fit$chains$sgibbs[j,],Ntr-1,r)
sigma[,,j] <- .expandSigma(fit$chains$sigErrGibbs[j], Sp, Z = Z, fit$chains$kgibbs[j,], REDUCT = T) #sigma
}
sigma_mean<-apply(sigma,c(1,2),mean)
err<-sum((sigma_mean-Sigma_true)^2)/(Sp*Sp)
rmspe<-fit$fit$rmspeAll
########Plot error graph
M_m<- as.vector(sigma_mean)
M_t<- as.vector(Sigma_true)
df_vs<- as.data.frame(M_m)
df_vs$M_t<- M_t
plot_vs <- ggplot(df_vs)+
aes(x = M_t, y = M_m)+geom_point()+geom_smooth(method = "lm") + geom_abline(intercept = -min(M_t), slope = 1, color="red")+
labs(title=paste0(" True vs estimated covariance parameters"), caption=paste0("Number of iterations: ",it," burnin: ",burn,"number of samples: ",nsamples,"S=",S," r=",r," true K=",K_t," type=",type))+ xlab("True")+ylab("Estimated")+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
#plot(plot_vs)
#pdf(paste0("plots/Plot-clusters_S",S,"r",r,"Ktr",K_t,"mod_type_",type,".pdf"))
#plot(p)
plot_list<-list()
plot_list<-list.append(plot_list,p)
if(type%in%c("1","2","4")){
#plot(p_alpha_1)
#plot(p_alpha_2)
plot_list<-list.append(plot_list,p_alpha_1)
plot_list<-list.append(plot_list,p_alpha_2)
}
if(type%in%c("4")){
# plot(p_sigma)
# plot(p_trace_sigma)
plot_list<-list.append(plot_list,p_sigma)
plot_list<-list.append(plot_list,p_trace_sigma)
}
if(type%in%c("0","1","2","3","4")){
#plot(pl_weigths)
plot_list<-list.append(plot_list,pl_weigths)
}
#plot(plot_vs)
plot_list<-list.append(plot_list,plot_vs)
# dev.off()
#chain=fit$chains$kgibbs
if(type%in%c("1","2","4")){
ind_alpha<- seq(1,length(alpha.chains), by =10)
alpha.chains_short<- alpha.chains[ind_alpha]
}
if(type%in%c("0","1","2","3","4")){
pN_chain<- pk_chains[-c(1:burn),(Ntr-1)]
ind_pn<- seq(1,length(pN_chain), by =10)
pN_chain_short<- pN_chain[ind_pn]
}
#pl_list=plot_list)
return(list(trace=trace_short,
idx=idx,K=fit$chains$kgibbs[it,],
alpha=alpha.DP,alpha.chains=alpha.chains_short,pk_val=pk, pkN=pN_chain_short,
coeff_t=Sigma_true,coeff_f=sigma_mean,
err=err,fit=rmspe))
}
####### Just one possible test case
#sim<-simulation_fun(Sp=50, Ntr=150, rval=3,nsamples=500, Ktrue=4,it=1000,burn=200,type=2)
# plot(as.vector(sim$coeff_t),as.vector(sim$coeff_f))
# x11()
# heatmap(sim$coeff_f)
# x11()
# heatmap(sim$coeff_t)
# plot(sim$trace)
# plot(sim$idx,sim$K)
#possible parameters to add in the loop:
# - type (T) of gjam to be fitted
# - n, the number of simulated normals
# - N, the truncation level
# - S, the number of species
# - K_t, the true number of clusters
###########Simulation for Continous data case :small S K=4###################################################
#####################################Simulation 2 K=10#######################################
####Small S, N==S, n=500
list=list()
list2=list()
list3=list()
list4=list()
list5=list()
list0=list()
data_list=list()
lk<-list()
S_vec<-c(100)
r_vec<-c(5)
k<-1
it<-1000
burn<-500
n_samples<-500
Ktr<-50
q<-20
#path<- "/mnt/workspace/Gjammod/"
path<-""
for(i in 1:length(S_vec)){
data_list=list()
list=list()
list2=list()
list3=list()
list4=list()
list5=list()
list0=list()
for(l in (1:2)){
data_list<- list.append(data_list,generate_data(Sp=S_vec[i],nsamples=n_samples,qval=q,Ktrue=Ktr))
names(data_list)[[l]]<-paste0("S_",S_vec[i],"_q_",q,"n_",n_samples,"_K_",Ktr,"_l",l)
}
save(data_list, file = paste0(path,"data/DS_S_",S_vec[i],"_q_",q,"_n_500_",Ktr,".Rda"))
print(i)
Ntrunc<-min(S_vec[i],150)
for(j in 1:length(r_vec)){
########GJAM model list########################
# l0<-list()
# l0<- mclapply(data_list,simulation_fun_oneDS,Sp=S_vec[i], Ntr=Ntrunc, q=q,rval=r_vec[j],nsamples=n_samples, Ktrue=Ktr,it=it,burn=burn,type="GJAM")
# list<-list.append(list,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_",S_vec[i],"_n_",n_samples,"_K",Ktr),l0))
# names(list)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_",S_vec[i],"_n_",n_samples,"_K",Ktr)
# save(list, file =paste0(path,"ODSim_smallS",S_vec[i],"K10_gjam.Rda"))
# ########gjam 0 model list########################
l00<-list()
l00<- lapply(data_list,simulation_fun_oneDS,Sp=S_vec[i], Ntr=Ntrunc, q=q,rval=r_vec[j],nsamples=n_samples, Ktrue=Ktr,it=it,burn=burn,type="0")
list0<-list.append(list0,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K_",Ktr),l00))
names(list0)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K_",Ktr)
save(list0, file = paste0(path,"ODSim_smallS",S_vec[i],"K10_gjam0.Rda"))
########gjam 1 model list########################
l2<-list()
l2<- lapply(data_list,simulation_fun_oneDS,Sp=S_vec[i], Ntr=150, q=q,rval=r_vec[j],nsamples=n_samples, Ktrue=Ktr,it=it,burn=burn,type="1")
list2<-list.append(list2,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr),l2))
names(list2)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr)
save(list2, file = paste0(path,"ODSim_smallS",S_vec[i],"K10_type1.Rda"))
########gjam 2 model list########################
l3<-list()
l3<- lapply(data_list,simulation_fun_oneDS,Sp=S_vec[i], Ntr=Ntrunc, q=q,rval=r_vec[j],nsamples=n_samples, Ktrue=Ktr,it=it,burn=burn,type="2")
list3<-list.append(list3,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr),l3))
names(list3)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr)
save(list3, file = paste0(path,"ODSim_smallS",S_vec[i],"K10_type2.Rda"))
########gjam 3 model list########################
l4<-list()
l4<- lapply(data_list,simulation_fun_oneDS,Sp=S_vec[i], Ntr=150, q=q,rval=r_vec[j],nsamples=n_samples, Ktrue=Ktr,it=it,burn=burn,type="3")
list4<-list.append(list4,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr),l4))
names(list4)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr)
save(list4, file = paste0(path,"ODSim_smallS",S_vec[i],"K10_type3.Rda"))
########gjam 4 model list########################
l5<-list()
l5<- lapply(data_list,simulation_fun_oneDS,Sp=S_vec[i], Ntr=150, q=q,rval=r_vec[j],nsamples=n_samples, Ktrue=Ktr,it=it,burn=burn,type="4")
list5<-list.append(list5,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr),l5))
names(list5)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr)
save(list5, file = paste0(path,"ODSim_smallS",S_vec[i],"K10_type4.Rda"))
k=k+1
}
# save(list, file =paste0("/mnt/workspace/Gjammod/ODSim_smallS",S_vec[i],"K10_gjam.Rda"))
#save(list0, file = paste0("/mnt/workspace/Gjammod/ODSim_smallS",S_vec[i],"K10_gjam0.Rda"))
# save(list2, file = paste0("/mnt/workspace/Gjammod/ODSim_smallS",S_vec[i],"K10_type1.Rda"))
# save(list3, file = paste0("/mnt/workspace/Gjammod/ODSim_smallS",S_vec[i],"K10_type2.Rda"))
# save(list4, file = paste0("/mnt/workspace/Gjammod/ODSim_smallS",S_vec[i],"K10_type3.Rda"))
#save(list5, file = paste0("/mnt/workspace/Gjammod/ODSim_smallS",S_vec[i],"K10_type4.Rda"))
}
dariamed/gjamed documentation built on Sept. 27, 2019, 5:31 p.m.
R Package Documentation
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rm(list=ls())
#setwd("~/Bureau/PY_comp0306/gjamed-master")
setwd("~/Documents/GitHub/gjamed")
########## Simulating the data
library(MASS)
library(repmis)
library(gjam)
library(rlist)
library(truncnorm)
#library(coda)
library(RcppArmadillo)
library(arm)
library(NLRoot)
library(Rcpp)
library(plyr)
library(ggplot2)
#library(ggsn)
library(parallel)
Rcpp::sourceCpp('src/cppFns.cpp')
source("R/gjamHfunctions_mod.R")
source("R/simple_gjam_0.R")
source("R/simple_gjam_1.R")
source("R/simple_gjam_2.R")
source("R/simple_gjam_3.R")
source("R/simple_gjam_4.R")
generate_data<-function(Sp=50,nsamples=500,qval=20,Ktrue=4){
S<-Sp
n<- nsamples
q<- qval
env<-runif(-50,50,n=n)
X<-cbind(1,poly(env,2)) #nxK
idx<-sample(S)
B_0<-seq(0,100,length.out=S)[idx]
B_1<-seq(0,100,length.out=S)[idx]
B_2<-seq(0,100,length.out=S)[idx]
B<-cbind(B_0,B_1,B_2) #SxK
L<-X%*%t(B) #nxS
K_t<- Ktrue
cat("True number of clusters : ",K_t,"\n")
A<-matrix(NA,nrow=ceiling(K_t),ncol=q)
for(i in 1:ceiling(K_t)){
A[i,]<-mvrnorm(n = 1,rep(0,q), Sigma=3*diag(q)) #Nxq short and skinny
}
idx<-sample((1:ceiling(K_t)),S,replace=T)
Lambda<-A[idx,] #Sxr tall and skinny
Sigma<-Lambda%*%t(Lambda)+0.1*diag(S) #SxS
Sigma_true<-Sigma
Y<-mvrnorm(n = n, mu=rep(0,S), Sigma=Sigma)
xdata<-as.data.frame(X[,-1])
colnames(xdata)<-c("env1","env2")
return(list(xdata=xdata, Y=Y,idx=idx,S_true=Sigma_true))
}
simulation_fun_oneDS<-function(data_set,Sp, Ntr, rval,nsamples=500, Ktrue,q=20, it=1000, burn=500,type="GJAM"){
S<-Sp
n<- nsamples
r <- rval
iterations<-it
#env<-runif(-50,50,n=n)
#X<-cbind(1,poly(env,2)) #nxK
#idx<-sample(S)
#B_0<-seq(0,100,length.out=S)[idx]
#B_1<-seq(0,100,length.out=S)[idx]
#B_2<-seq(0,100,length.out=S)[idx]
#B<-cbind(B_0,B_1,B_2) #SxK
#L<-X%*%t(B) #nxS
K=sum(S/(S+(1:S)-1)) #104, his prior number of clusters when alpha=S
if(type=="GJAM"){ cat("Prior expected number of clusters : ",K,"\n")}
else{cat("Prior expected number of clusters : ",Ktrue,"\n")}
K_t= Ktrue
cat("True number of clusters : ",K_t,"\n")
xdata<-data_set$xdata
Y<-data_set$Y
idx<- data_set$idx
Sigma_true<- data_set$S_true
formula<-as.formula(~env1+env2)
if(type=="GJAM"){
rl <- list(r = r, N =Ntr-1)
ml<-list(ng=it,burnin=burn,typeNames='CON',reductList=rl)
fit<-gjam(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-NULL
alpha.DP<-S
pk_chains<-NULL
pk<-NULL
alpha.chains_short<-NULL
pN_chain_short<-NULL
}
if(type=="0"){
#func<-function(x) {sum(x/(x+(1:S)-1))-K_t}
#alpha.DP<-.bisec(func,0.01,100)
alpha.DP<-S
rl <- list(r = r, N =Ntr-1,alpha.DP=alpha.DP)
ml<-list(ng=it,burnin=burn,typeNames='CON',reductList=rl)
fit<-.gjam0(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-NULL
alpha.chains_short<-NULL
pk_chains<- fit$chains$pk_g
}
if(type=="1"){
func<-function(x) {sum(x/(x+(1:S)-1))-K_t}
alpha.DP<-.bisec(func,0.01,100)
shape=((alpha.DP)^2)/20
rate=alpha.DP/20
rl <- list(r = r, N = Ntr-1, rate=rate,shape=shape)
ml<-list(ng=it,burnin=burn,typeNames='CON',reductList=rl)
fit<-.gjam_1(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-fit$chains$alpha.DP_g
pk_chains<- fit$chains$pk_g
}
if(type=="2"){
func<-function(x) {sum(x/(x+(1:S)-1))-K_t}
alpha.DP<-.bisec(func,0.01,100)
shape=((alpha.DP)^2)/20
rate=alpha.DP/20
rl <- list(r = r, N = Ntr-1, rate=rate,shape=shape,V=1)
ml<-list(ng=it,burnin=burn,typeNames='CON',reductList=rl)
fit<-.gjam_2(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-fit$chains$alpha.DP_g
pk_chains<- fit$chains$pk_g
}
if(type=="3"){
eps=0.01
sigma_py<-0.25
funcPY_root<-function(x) {(x/sigma_py)*(prod((x+sigma_py+c(1:S) -1)/(x+c(1:S) -1))-1) - K_t}
alpha.PY<-.bisec(funcPY_root,0.0001,100)
N_eps<-floor(.compute_tau_mean(sigma_py,alpha.PY,eps) + 2*.compute_tau_var(sigma_py,alpha.PY,eps))
rl <- list(r = r, N = N_eps, sigma_py=sigma_py, alpha=alpha.PY)
ml<-list(ng=it,burnin=burn,typeNames='CON',reductList=rl)
fit<-.gjam_3(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-NULL
alpha.chains_short<-NULL
pk_chains<- fit$chains$pk_g
alpha.DP<-alpha.PY
Ntr<-N_eps+1
}
if(type=="4"){
eps=0.1
alp_sig<-as.data.frame(matrix(NA,nrow=20,ncol=3))
colnames(alp_sig)<-c("alpha","sigma","is_less_150")
alp_sig$sigma=seq(0.05,0.4,length.out = 20)
#loop to run bisecetion on a grid for sigma
for(i in 1:20){
####corrected added -1
func<-function(x) {(x/alp_sig[i,"sigma"])*(prod((x+alp_sig[i,"sigma"]+c(1:S)-1)/(x+c(1:S) -1))-1) - K_t}
alp_sig[i,"alpha"]<-.bisec(func,0.01,100)
N_eps<-floor(.compute_tau_mean(alp_sig[i,"sigma"], alp_sig[i,"alpha"],eps) + 2*.compute_tau_var(alp_sig[i,"sigma"], alp_sig[i,"alpha"],eps))
ifelse(N_eps<=150,alp_sig[i,"is_less_150"]<-T,alp_sig[i,"is_less_150"]<-F)
N_eps
}
if(sum(alp_sig$is_less_150==T)==0) cat("!! no choice under N=150, need to recheck!!!")
k<-max(which(alp_sig$is_less_150==T)) #max sigma s.t. N<150
sigma_py<-alp_sig[k,"sigma"]
alpha.PY<-alp_sig[k,"alpha"]
#fixing hyperparameters
ro.disc=1-2* sigma_py
shape=((alpha.PY)^2)/10
rate=alpha.PY/10
# 95% quantile of alpha
alpha.max=qgamma(.95, shape=shape, rate=rate)
#alpha.max_val<-5
sigma_py_max<-0.5
N_eps<-floor(.compute_tau_mean_large_dim(sigma_py_max,alpha.max,eps) + 2*.compute_tau_var_large_dim(sigma_py_max,alpha.max,eps))
rl <- list(r = r, N = N_eps,rate=rate,shape=shape,V1=1,ro.disc=ro.disc) #here to modify N
ml<-list(ng=it,burnin=burn,typeNames='CON',reductList=rl)
fit<-.gjam_4(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-fit$chains$alpha.PY_g
sigma.chains<-fit$chains$discount.PY_g
pk_chains<- fit$chains$pk_g
Ntr<-N_eps+1
alpha.DP<-alpha.PY
}
trace<-apply(fit$chains$kgibbs,1,function(x) length(unique(x)))
ind_trace<- seq(1,it,by=5)
trace_short<- trace[ind_trace]
df<-as.data.frame(trace)
df$iter<-1:it
#plot(apply(fit$chains$kgibbs,1,function(x) length(unique(x))))
p<-ggplot(df, aes(y=trace, x=iter)) + geom_point() +
labs(title=paste0("Trace plot for the number of groups K for S=",S," r=",r," true K=",K_t," type=",type), caption=paste0("Number of iterations: ",it," burnin: ",burn,"number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))+
geom_hline(yintercept = Ktrue,color = "red")
#plot(p)
#####Weights plot
if(type%in%c("0","1","2","3","4")){
pk<- apply(fit$chains$pk_g[-c(1:burn),],2,mean)
last_pk<- round(pk[Ntr-1],3)
df_weights <- data.frame(matrix(NA, nrow = Ntr-1, ncol =1))
df_weights$pw<-pk
df_weights$tr<-1:(Ntr-1)
pl_weigths<- ggplot(df_weights, aes(x=tr, y=pw)) +
geom_segment( aes(x=tr,xend=tr,y=0,yend=pw)) +
geom_point( size=0.5, color="red", fill=alpha("blue", 0.3), alpha=0.4, shape=21, stroke=2)+ labs(title=paste0("Weights for the case: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr, " pN=",last_pk), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
# pl_weigths
}
#####Alpha plot
if(type%in%c("1","2","4")){
df_alpha <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
df_alpha$alpha<- alpha.chains[-c(1:burn)]
df_alpha$type<- "posterior"
df_alpha_prior <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
#df_alpha_prior$alpha<- rgamma(it-burn, shape, rate)
alpha_seq= seq(min(alpha.chains[-c(1:burn)]),max(alpha.chains[-c(1:burn)]),length=it-burn)
df_alpha_prior$alpha <- dgamma(alpha_seq,rate,shape)
df_alpha_prior$type<- "prior"
df_alpha_all<- rbind(df_alpha[-1,],df_alpha_prior[-1,])
###Compute mean
mu <- ddply(df_alpha_all, "type", summarise, grp.mean=mean(alpha))
mu$grp.mean[which(mu$type=="prior")]=alpha.DP
p_alpha_1<- ggplot(df_alpha_all, aes(x=alpha, color=type)) + geom_vline(data=mu, aes(xintercept=grp.mean, color=type),linetype="dashed")+
geom_density()+labs(title=paste0("Distribution alpha: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
# p_alpha_1
p_alpha_2<- ggplot(df_alpha, aes(x=alpha)) + geom_vline(data=mu, aes(xintercept=grp.mean, color=type),linetype="dashed")+
geom_density(color="red")+labs(title=paste0("Posterior distribution for alpha"), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples," S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))+
scale_color_manual(name = c("Legend"), values = c("prior"="#9999FF", "posterior"= "#FF6666"), labels=c("posterior mean","prior mean"))
# p_alpha_2
}
#######Sigma plot
if(type%in%c("4")){
df_sigma <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
df_sigma$sigma<- sigma.chains[-c(1:burn)]
###Compute mean
mu <- ddply(df_sigma, type, summarise, grp.mean=mean(sigma))
p_sigma<- ggplot(df_sigma, aes(x=sigma)) + geom_vline(data=mu, aes(xintercept=grp.mean),linetype="dashed")+
geom_density()+labs(title=paste0("Distribution sigma: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
# p_sigma
dfs<-as.data.frame(sigma.chains)
dfs$iter<-1:it
#plot(apply(fit$chains$kgibbs,1,function(x) length(unique(x))))
p_trace_sigma<-ggplot(dfs, aes(y=sigma.chains, x=iter)) + geom_point() +
labs(title=paste0("Trace plot for the sigma for S=",S," r=",r," true K=",K_t," type=",type), caption=paste0("Number of iterations: ",it," burnin: ",burn,"number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
# p_trace_sigma
}
N_dim<-(it-burn)
sigma<-array(dim=c(Sp,Sp,N_dim))
for(j in 1:N_dim){
K<-fit$chains$kgibbs[j,]
Z <- matrix(fit$chains$sgibbs[j,],Ntr-1,r)
sigma[,,j] <- .expandSigma(fit$chains$sigErrGibbs[j], Sp, Z = Z, fit$chains$kgibbs[j,], REDUCT = T) #sigma
}
sigma_mean<-apply(sigma,c(1,2),mean)
err<-sum((sigma_mean-Sigma_true)^2)/(Sp*Sp)
rmspe<-fit$fit$rmspeAll
########Plot error graph
M_m<- as.vector(sigma_mean)
M_t<- as.vector(Sigma_true)
df_vs<- as.data.frame(M_m)
df_vs$M_t<- M_t
plot_vs <- ggplot(df_vs)+
aes(x = M_t, y = M_m)+geom_point()+geom_smooth(method = "lm") + geom_abline(intercept = -min(M_t), slope = 1, color="red")+
labs(title=paste0(" True vs estimated covariance parameters"), caption=paste0("Number of iterations: ",it," burnin: ",burn,"number of samples: ",nsamples,"S=",S," r=",r," true K=",K_t," type=",type))+ xlab("True")+ylab("Estimated")+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
#plot(plot_vs)
#pdf(paste0("plots/Plot-clusters_S",S,"r",r,"Ktr",K_t,"mod_type_",type,".pdf"))
#plot(p)
plot_list<-list()
plot_list<-list.append(plot_list,p)
if(type%in%c("1","2","4")){
#plot(p_alpha_1)
#plot(p_alpha_2)
plot_list<-list.append(plot_list,p_alpha_1)
plot_list<-list.append(plot_list,p_alpha_2)
}
if(type%in%c("4")){
# plot(p_sigma)
# plot(p_trace_sigma)
plot_list<-list.append(plot_list,p_sigma)
plot_list<-list.append(plot_list,p_trace_sigma)
}
if(type%in%c("0","1","2","3","4")){
#plot(pl_weigths)
plot_list<-list.append(plot_list,pl_weigths)
}
#plot(plot_vs)
plot_list<-list.append(plot_list,plot_vs)
# dev.off()
#chain=fit$chains$kgibbs
if(type%in%c("1","2","4")){
ind_alpha<- seq(1,length(alpha.chains), by =10)
alpha.chains_short<- alpha.chains[ind_alpha]
}
if(type%in%c("0","1","2","3","4")){
pN_chain<- pk_chains[-c(1:burn),(Ntr-1)]
ind_pn<- seq(1,length(pN_chain), by =10)
pN_chain_short<- pN_chain[ind_pn]
}
#pl_list=plot_list)
return(list(trace=trace_short,
idx=idx,K=fit$chains$kgibbs[it,],
alpha=alpha.DP,alpha.chains=alpha.chains_short,pk_val=pk, pkN=pN_chain_short,
coeff_t=Sigma_true,coeff_f=sigma_mean,
err=err,fit=rmspe))
}
####### Just one possible test case
#sim<-simulation_fun(Sp=50, Ntr=150, rval=3,nsamples=500, Ktrue=4,it=1000,burn=200,type=2)
# plot(as.vector(sim$coeff_t),as.vector(sim$coeff_f))
# x11()
# heatmap(sim$coeff_f)
# x11()
# heatmap(sim$coeff_t)
# plot(sim$trace)
# plot(sim$idx,sim$K)
#possible parameters to add in the loop:
# - type (T) of gjam to be fitted
# - n, the number of simulated normals
# - N, the truncation level
# - S, the number of species
# - K_t, the true number of clusters
###########Simulation for Continous data case :small S K=4###################################################
#####################################Simulation 2 K=10#######################################
####Small S, N==S, n=500
list=list()
list2=list()
list3=list()
list4=list()
list5=list()
list0=list()
data_list=list()
lk<-list()
S_vec<-c(100)
r_vec<-c(5)
k<-1
it<-1000
burn<-500
n_samples<-500
Ktr<-50
q<-20
#path<- "/mnt/workspace/Gjammod/"
path<-""
for(i in 1:length(S_vec)){
data_list=list()
list=list()
list2=list()
list3=list()
list4=list()
list5=list()
list0=list()
for(l in (1:2)){
data_list<- list.append(data_list,generate_data(Sp=S_vec[i],nsamples=n_samples,qval=q,Ktrue=Ktr))
names(data_list)[[l]]<-paste0("S_",S_vec[i],"_q_",q,"n_",n_samples,"_K_",Ktr,"_l",l)
}
save(data_list, file = paste0(path,"data/DS_S_",S_vec[i],"_q_",q,"_n_500_",Ktr,".Rda"))
print(i)
Ntrunc<-min(S_vec[i],150)
for(j in 1:length(r_vec)){
########GJAM model list########################
# l0<-list()
# l0<- mclapply(data_list,simulation_fun_oneDS,Sp=S_vec[i], Ntr=Ntrunc, q=q,rval=r_vec[j],nsamples=n_samples, Ktrue=Ktr,it=it,burn=burn,type="GJAM")
# list<-list.append(list,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_",S_vec[i],"_n_",n_samples,"_K",Ktr),l0))
# names(list)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_",S_vec[i],"_n_",n_samples,"_K",Ktr)
# save(list, file =paste0(path,"ODSim_smallS",S_vec[i],"K10_gjam.Rda"))
# ########gjam 0 model list########################
l00<-list()
l00<- lapply(data_list,simulation_fun_oneDS,Sp=S_vec[i], Ntr=Ntrunc, q=q,rval=r_vec[j],nsamples=n_samples, Ktrue=Ktr,it=it,burn=burn,type="0")
list0<-list.append(list0,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K_",Ktr),l00))
names(list0)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K_",Ktr)
save(list0, file = paste0(path,"ODSim_smallS",S_vec[i],"K10_gjam0.Rda"))
########gjam 1 model list########################
l2<-list()
l2<- lapply(data_list,simulation_fun_oneDS,Sp=S_vec[i], Ntr=150, q=q,rval=r_vec[j],nsamples=n_samples, Ktrue=Ktr,it=it,burn=burn,type="1")
list2<-list.append(list2,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr),l2))
names(list2)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr)
save(list2, file = paste0(path,"ODSim_smallS",S_vec[i],"K10_type1.Rda"))
########gjam 2 model list########################
l3<-list()
l3<- lapply(data_list,simulation_fun_oneDS,Sp=S_vec[i], Ntr=Ntrunc, q=q,rval=r_vec[j],nsamples=n_samples, Ktrue=Ktr,it=it,burn=burn,type="2")
list3<-list.append(list3,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr),l3))
names(list3)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr)
save(list3, file = paste0(path,"ODSim_smallS",S_vec[i],"K10_type2.Rda"))
########gjam 3 model list########################
l4<-list()
l4<- lapply(data_list,simulation_fun_oneDS,Sp=S_vec[i], Ntr=150, q=q,rval=r_vec[j],nsamples=n_samples, Ktrue=Ktr,it=it,burn=burn,type="3")
list4<-list.append(list4,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr),l4))
names(list4)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr)
save(list4, file = paste0(path,"ODSim_smallS",S_vec[i],"K10_type3.Rda"))
########gjam 4 model list########################
l5<-list()
l5<- lapply(data_list,simulation_fun_oneDS,Sp=S_vec[i], Ntr=150, q=q,rval=r_vec[j],nsamples=n_samples, Ktrue=Ktr,it=it,burn=burn,type="4")
list5<-list.append(list5,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr),l5))
names(list5)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_K",Ktr)
save(list5, file = paste0(path,"ODSim_smallS",S_vec[i],"K10_type4.Rda"))
k=k+1
}
# save(list, file =paste0("/mnt/workspace/Gjammod/ODSim_smallS",S_vec[i],"K10_gjam.Rda"))
#save(list0, file = paste0("/mnt/workspace/Gjammod/ODSim_smallS",S_vec[i],"K10_gjam0.Rda"))
# save(list2, file = paste0("/mnt/workspace/Gjammod/ODSim_smallS",S_vec[i],"K10_type1.Rda"))
# save(list3, file = paste0("/mnt/workspace/Gjammod/ODSim_smallS",S_vec[i],"K10_type2.Rda"))
# save(list4, file = paste0("/mnt/workspace/Gjammod/ODSim_smallS",S_vec[i],"K10_type3.Rda"))
#save(list5, file = paste0("/mnt/workspace/Gjammod/ODSim_smallS",S_vec[i],"K10_type4.Rda"))
}
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