#read the appropriate version of the package
source("https://raw.githubusercontent.com/aliaksah/EMJMCMC2016/master/R/the_mode_jumping_package2.r")
#define some function for cleaning up after parallel computations
library(inline)
includes = '#include <sys/wait.h>'
code = 'int wstat; while (waitpid(-1, &wstat, WNOHANG) > 0) {};'
wait = cfunction(body=code, includes=includes, convention='.C')
#define the function estimating parameters of a given Gaussian logic regression with Jeffrey's prior
estimate.logic.lm = function(formula, data, n, m, r = 1)
{
out = lm(formula = formula,data = data)
p = out$rank
fmla.proc=as.character(formula)[2:3]
fobserved = fmla.proc[1]
fmla.proc[2]=stri_replace_all(str = fmla.proc[2],fixed = " ",replacement = "")
fmla.proc[2]=stri_replace_all(str = fmla.proc[2],fixed = "\n",replacement = "")
fparam =stri_split_fixed(str = fmla.proc[2],pattern = "+",omit_empty = F)[[1]]
sj=(stri_count_fixed(str = fparam, pattern = "&"))
sj=sj+(stri_count_fixed(str = fparam, pattern = "|"))
sj=sj+1
Jprior = prod(factorial(sj)/((m^sj)*2^(2*sj-2)))
mlik = (-BIC(out)+2*log(Jprior) + 2*p*log(r)+n)/2
if(mlik==-Inf)
mlik = -10000
return(list(mlik = mlik,waic = AIC(out)-n , dic = BIC(out)-n,summary.fixed =list(mean = coef(out))))
}
#define the function for perfroming parallel computations
parall.gmj = mclapply
#define the function simplifying logical expressions at the end of the search
simplifyposteriors=function(X,posteriors,th=0.0001,thf=0.5)
{
posteriors=posteriors[-which(posteriors[,2]<th),]
rhash=hash()
for(i in 1:length(posteriors[,1]))
{
expr=posteriors[i,1]
print(expr)
res=model.matrix(data=X,object = as.formula(paste0("Y1~",expr)))
res[,1]=res[,1]-res[,2]
ress=c(stri_flatten(res[,1],collapse = ""),stri_flatten(res[,2],collapse = ""),posteriors[i,2],expr)
if(!(ress[1] %in% values(rhash)||(ress[2] %in% values(rhash))))
rhash[[ress[1]]]=ress
else
{
if(ress[1] %in% keys(rhash))
{
rhash[[ress[1]]][3]= (as.numeric(rhash[[ress[1]]][3]) + as.numeric(ress[3]))
if(stri_length(rhash[[ress[1]]][4])>stri_length(expr))
rhash[[ress[1]]][4]=expr
}
else
{
rhash[[ress[2]]][3]= (as.numeric(rhash[[ress[2]]][3]) + as.numeric(ress[3]))
if(stri_length(rhash[[ress[2]]][4])>stri_length(expr))
rhash[[ress[2]]][4]=expr
}
}
}
res=as.data.frame(t(values(rhash)[c(3,4),]))
res$V1=as.numeric(as.character(res$V1))
res=res[which(res$V1>thf),]
res=res[order(res$V1, decreasing = T),]
clear(rhash)
rm(rhash)
res[which(res[,1]>1),1]=1
colnames(res)=c("posterior","tree")
return(res)
}
#define number of simulations
MM = 100
#define number of threads to be used
M = 32
#define the size of the simulated samples
NM= 1000
#define \k_{max} + 1 from the paper
compmax = 16
#define treshold for preinclusion of the tree into the analysis
th=(10)^(-5)
#define a final treshold on the posterior marginal probability for reporting a tree
thf=0.05
#define a function performing the map step for a given thread
runpar=function(vect)
{
set.seed(as.integer(vect[22]))
do.call(runemjmcmc, vect[1:21])
vals=values(hashStat)
fparam=mySearch$fparam
cterm=max(vals[1,],na.rm = T)
ppp=mySearch$post_proceed_results_hash(hashStat = hashStat)
post.populi=sum(exp(values(hashStat)[1,][1:NM]-cterm),na.rm = T)
clear(hashStat)
rm(hashStat)
rm(vals)
return(list(post.populi = post.populi, p.post = ppp$p.post, cterm = cterm, fparam = fparam))
}
#perform MM runs of GMJMCMC on M threads each
for(j in 1:MM)
{
#prepare the data for simulation j
set.seed(j)
X1= as.data.frame(array(data = rbinom(n = 50*1000,size = 1,prob = runif(n = 50*1000,0,1)),dim = c(1000,50)))
Y1=rnorm(n = 1000,mean = 1+0.7*(X1$V1*X1$V4) + 0.8896846*(X1$V8*X1$V11)+1.434573*(X1$V5*X1$V9),sd = 1)
X1$Y1=Y1
#specify the initial formula
formula1 = as.formula(paste(colnames(X1)[51],"~ 1 +",paste0(colnames(X1)[-c(51)],collapse = "+")))
data.example = as.data.frame(X1)
#specify tuning parameters of the algorithm for exploring the space of Bayesian logic regressions of interest
#notice that allow_offsprings=1 corresponds to the GMJMCMC algorithm for Bayesian logic regression
vect=list(formula = formula1,data = X1,estimator = estimate.logic.lm,estimator.args = list(data = data.example,n = 1000, m = 50),recalc_margin = 250, save.beta = F,interact = T,relations = c("","lgx2","cos","sigmoid","tanh","atan","erf"),relations.prob =c(0.4,0.0,0.0,0.0,0.0,0.0,0.0),interact.param=list(allow_offsprings=1,mutation_rate = 300,last.mutation = 5000, max.tree.size = 4, Nvars.max = (compmax-1),p.allow.replace=0.9,p.allow.tree=0.2,p.nor=0,p.and = 0.9),n.models = 10000,unique = T,max.cpu = 4,max.cpu.glob = 4,create.table = F,create.hash = T,pseudo.paral = T,burn.in = 50,outgraphs=F,print.freq = 1000,advanced.param = list(
max.N.glob=as.integer(10),
min.N.glob=as.integer(5),
max.N=as.integer(3),
min.N=as.integer(1),
printable = F))
params = list(vect)[rep(1,M)]
#specify additional information to be used on different threads (e.g. seeds)
for(i in 1:M)
{
params[[i]]$cpu=i
params[[i]]$simul="scenario_1_"
params[[i]]$simid=j
}
#perform garbage collection
gc()
#explore Byesian logic regression on M threads in parallel using the GMJMCMC algorithm
print(paste0("begin simulation ",j))
results=parall.gmj(X = params,FUN = runpar,mc.preschedule = F, mc.cores = M)
#clean up
gc()
wait()
#prepare the data structures for final analysis of the runs
resa=array(data = 0,dim = c(compmax,M*3))
post.popul = array(0,M)
max.popul = array(0,M)
nulls=NULL
not.null=1
#check which threads had non-zero exit status
for(k in 1:M)
{
if(length(results[[k]]$cterm)==0)
{
nulls=c(nulls,k)
next
}
else
{
not.null = k
}
}
#for all of the successful runs collect the results into the corresponding data structures
for(k in 1:M)
{
if(k %in% nulls)
{
results[[k]]=results[[not.null]]
}
max.popul[k]=results[[k]]$cterm
post.popul[k]=results[[k]]$post.populi
resa[,k*3-2]=c(results[[k]]$fparam,"Post.Gen.Max")
resa[,k*3-1]=c(results[[k]]$p.post,results[[k]]$cterm)
resa[,k*3]=rep(post.popul[k],length(results[[k]]$p.post)+1)
}
#delete the unused further variables and perfrom garbage collection
rm(results)
gc()
#renormalize estimates of the marginal inclusion probabilities
#based on all of the runs
ml.max=max(max.popul)
post.popul=post.popul*exp(-ml.max+max.popul)
p.gen.post=post.popul/sum(post.popul)
hfinal=hash()
for(ii in 1:M)
{
resa[,ii*3]=p.gen.post[ii]*as.numeric(resa[,ii*3-1])
resa[length(resa[,ii*3]),ii*3]=p.gen.post[ii]
if(p.gen.post[ii]>0)
{
for(jj in 1:(length(resa[,ii*3])-1))
{
if(resa[jj,ii*3]>0)
{
#print(paste0(ii," and ",jj))
if(as.integer(has.key(hash = hfinal,key =resa[jj,ii*3-2]))==0)
hfinal[[resa[jj,ii*3-2]]]=as.numeric(resa[jj,ii*3])
else
hfinal[[resa[jj,ii*3-2]]]=hfinal[[resa[jj,ii*3-2]]]+as.numeric(resa[jj,ii*3])
}
}
}
}
posteriors=values(hfinal)
#delete the unused further variables
clear(hfinal)
rm(hfinal)
rm(resa)
rm(post.popul)
rm(max.popul)
#simplify the found trees and their posteriors
posteriors=as.data.frame(posteriors)
posteriors=data.frame(X=row.names(posteriors),x=posteriors$posteriors)
posteriors$X=as.character(posteriors$X)
tryCatch({
res1=simplifyposteriors(X = X1,posteriors = posteriors, th,thf)
write.csv(x =res1,row.names = F,file = paste0("post1etaOld_",j,".csv"))},error = function(err){
print("error")
write.csv(x =posteriors,row.names = F,file = paste0("posteriors1etaOld_",j,".csv"))},finally = {
print(paste0("end simulation ",j))
})
#delete the unused further variables and perfrom garbage collection
rm(X1)
rm(data.example)
rm(vect)
rm(params)
gc()
print(paste0("end simulation ",j))
}
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