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gaussian_categorical.R
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gaussian_categorical.R
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setwd("~/GitHub/GraphicalModels-BayesStat")
source("utilityFunctions.R")
source("cutoff_utility.R")
source("gaussian.R")
library(CholWishart)
library(tmvtnorm)
#############################################################
###############MH for categorical gaussian###################
#############################################################
# We need to add latent Gaussian Z and the cutoffs tetha
# teta will be sample with a MH step
# Z will be sampled from a truncated gaussian according to the cutoffs tetha
# once we have z we just follows the same procedure as for the pure gaussian case
MetropolisHastingsGaussianCategorical = function(data, initialCandidate, n.iter, burnin = 0, thin = 1, prior, p = NULL, b = NULL, algorithm="gibbs"){
# We check that the passed parameters are correct
if(!prior %in% c("Uniform","Binomial","Beta-Binomial")){
stop("prior should be either 'Uniform', 'Binomial' or 'Beta-Binomial'!")
}
if(!isDecomposable(initialCandidate)){
stop("Initial candidate graph should be decomposable!")
}
currentCandidate = initialCandidate
b = 1 #degress of freedom of the Hyperinverse Whishart
n = dim(data)[1]
D = 10 * diag(1, dim(data)[2]) #parameter D of the Hyperinverse Whishart
x = data.matrix(data)
tau_prior = 10 #std deviation prior on the cutoffs vector
#initialization
tetha = rep(0, dim(x)[2]) #initialize tetha with zeros
Z = generate_Z(Sigma=D, lower=lower_bounds(tetha,x), upper=upper_bounds(tetha,x), algorithm=algorithm)
Sigma = D + t(Z)%*%Z
D_star = Sigma #That's the parameter of the posterior for the Sigma
# Run the burnin iterations
if(burnin!=0){
message("BURN-IN")
progressBarBI = txtProgressBar(min = 0, max = burnin, initial = 0, style = 3)
for(i in 1:burnin){
setTxtProgressBar(progressBarBI,i)
tetha = MH_tetha(Sigma=Sigma, x=x, tau_prior=tau_prior, tetha=tetha) #updata tetha vector with a MH step
Sigma = update_Sigma(df=b+n, Dstar=D_star, adj=currentCandidate) #update Sigma
Z = generate_Z(Sigma=Sigma, lower=lower_bounds(tetha,x), upper=upper_bounds(tetha,x), algorithm=algorithm)
D_star = D + t(Z)%*%Z #update D_star for the HWS
newCandidate = newGraphProposal(currentCandidate)
num = logMarginalLikelihoodGaussian(newCandidate, Z, b, D, D_star=D_star)
den = logMarginalLikelihoodGaussian(currentCandidate, Z, b, D, D_star=D_star)
marginalRatio = exp(num - den)
priorRatio = switch(prior, "Uniform" = 1, "Binomial" = binomialPrior(currentCandidate,newCandidate,p), "Beta-Binomial" = betaBinomialPrior(currentCandidate,newCandidate,a,b))
acceptanceProbability = min(marginalRatio * priorRatio,1)
accepted = rbern(1,acceptanceProbability)
if(accepted == 1){
currentCandidate = newCandidate
}
}
close(progressBarBI)
}
# Run the chain
message("Metropolis-Hastings")
progressBar = txtProgressBar(min = 0, max = n.iter, initial = 0, style = 3)
chain = list()
c = 0
for(i in 1:n.iter){
setTxtProgressBar(progressBar,i)
tetha = MH_tetha(Sigma=Sigma, x=x, tau_prior=tau_prior, tetha=tetha) #updata tetha vector with a MH step
Sigma = update_Sigma(df=b+n, Dstar=D_star, adj=currentCandidate) #update Sigma
Z = generate_Z(Sigma=Sigma, lower=lower_bounds(tetha,x), upper=upper_bounds(tetha,x), algorithm="gibbs")
D_star = D + t(Z)%*%Z #update D_star for the HWS
newCandidate = newGraphProposal(currentCandidate)
num = logMarginalLikelihoodGaussian(newCandidate, Z, b, D, D_star=D_star)
den = logMarginalLikelihoodGaussian(currentCandidate, Z, b, D, D_star=D_star)
marginalRatio = exp(num - den)
priorRatio = switch(prior, "Uniform" = 1, "Binomial" = binomialPrior(currentCandidate,newCandidate,p), "Beta-Binomial" = betaBinomialPrior(currentCandidate,newCandidate,a,b))
acceptanceProbability = min(marginalRatio * priorRatio,1)
accepted = rbern(1,acceptanceProbability)
c = c + accepted
if(accepted == 1){
currentCandidate = newCandidate
}
if(i %% thin == 0){
chain[[i/thin]] = currentCandidate
}
}
if(burnin!=0){
close(progressBarBI)
}
cat(paste0("\nThe average acceptance rate is: ", as.character(c / n.iter),"\n"))
return(chain)
}
update_Sigma = function(df, Dstar, adj){
inv.covariance = rgwish(n = 1, adj = adj, b = df, D = Dstar)
covariance = solve(inv.covariance)
return(covariance)
}