#R<code4.txt --no-save>code4output.txt &
#This is the unix command to run this code in the background and save the output in the file code4output.txt

postscript("code4plot.ps")
par(mfrow=c(1,1),cex=1.5,cex.axis=1.5,cex.lab=1.5)

set.seed(4444, kind = NULL)

repeat.times<-100

q<-.2
iterations<-1000
n<-5000
d<-20
m<-1000
#m is the size of the hold-out sample (i.e., the test sample)


misclass.store<-matrix(0,repeat.times,iterations)



bayeserror.store<-rep(0,repeat.times)
nnerror.store<-rep(0,repeat.times)
rferror.store<-rep(0,repeat.times)

library(class)
library(rpart)

#You can also try using Random Forests for comparison by uncommenting the code provided later
#I commented it out because Random Forests is not part of the basic R package and must be installed separately
#I put mine in the directory "temp" using the following commands (from within R)
#options(CRAN = "http://cran.us.r-project.org/")
#install.packages("randomForest",lib="temp")
#library(randomForest, lib.loc="temp")


for (iui in 1:repeat.times){

x<-matrix(0,n,d)
for (ddd in 1:d){
x[,ddd]<-runif(n)
}

hold.out.x<-matrix(0,m,d)
for (k in 1:d) {
hold.out.x[,k]<-runif(m)
}

y<-rep(0,n)
for (i in 1:n){
y[i]<-1*(runif(1)<q)
}

hold.out.y<-rep(0,m)
for (i in 1:(m)){
hold.out.y[i]<-1*(runif(1)<q)
}


#error for bayes rule
bayespred<-rep(0,m)
for (i in 1:(m)){
bayespred[i]<-0
}

bayeserror<-1-sum((as.numeric(bayespred)==hold.out.y))/length(bayespred)
bayeserror.store[iui]<-bayeserror

#nearest neighbor
fit<-knn(x,hold.out.x,y,k=1,prob=T)
ppp<-attributes(fit)$prob
ppp[as.numeric(fit)==1]<-1-ppp[as.numeric(fit)==1]
nnerror<-(1-sum((ppp==hold.out.y)/length(ppp)))
nnerror.store[iui]<-nnerror


#AdaBoost

y<-(-1)+2*y
hold.out.y<-(-1)+2*hold.out.y
f<-rep(0,n)
hold.out.f<-0
i<-1
te<-rep(0,iterations)
misclass<-rep(0,iterations)

while(i<=iterations){
w<-exp(-y*f)

w<-w/sum(w)

treee<-rpart(y~.,data.frame(x),w,method="class",
control=rpart.control(minsplit=0,minbucket=0,cp=-1,maxcompete=0, maxsurrogate=0, usesurrogate=0, xval=0,maxdepth=8))

gmin<-(-1)+2*(predict(treee,data.frame(x),type="prob")[,1]<
predict(treee,data.frame(x),type="prob")[,2])

hold.out.gmin<-(-1)+2*(predict(treee,data.frame(hold.out.x),type="prob")[,1]<
predict(treee,data.frame(hold.out.x),type="prob")[,2])

e<-sum(w*(1-(y==gmin)))

alpha<-.5*log ( (1-e) / e )

hold.out.f<-hold.out.f+alpha*hold.out.gmin
f<-f+alpha*gmin

te[i]<-sum(1*f*y<0)/n

misclass[i]<-sum(1*hold.out.f*hold.out.y<0)/length(hold.out.f)

print(c(i,te[i],misclass[i]))

i<-i+1


}

#Random Forests (you need to install the package as described above if you want to use this) 
#y<-as.factor(y)
#rf<-randomForest(x, y)
#classest<-predict(rf,hold.out.x)
#rferror<-(1-sum((classest==hold.out.y)/length(hold.out.y)))
#rferror.store[iui]<-rferror



print("bayes error")
print(bayeserror)

print("nn error")
print(nnerror)

#print("random Forest error")
#print(rferror)

misclass.store[iui,]<-misclass

}

mean.misclass<-apply(misclass.store,2,mean)

plot(seq(1,iterations),mean.misclass,ylim=c(.20,.26),xlab="AdaBoost Iterations",ylab="Misclassification Error",
type="n",main="")
lines(seq(1,iterations),mean.misclass,col="red")

dev.off()


print("###############################################################")
print("Nearest Neighbor Mean and Standard Deviation")
print(mean(nnerror.store))
print(sqrt(var(nnerror.store)))

#print("Random Forests Mean and Standard Deviation")
#print(mean(rferror.store))
#print(sqrt(var(rferror.store)))

print("Bayes Error Mean and Standard Deviation")
print(mean(bayeserror.store))
print(sqrt(var(bayeserror.store)))

print("AdaBoost Final Mean and Standard Deviation")
print(mean(misclass.store[,iterations]))
print(sqrt(var(misclass.store[,iterations])))

print("AdaBoost First Iteration Mean and Standard Deviation")
print(mean(misclass.store[,1]))
print(sqrt(var(misclass.store[,1])))

print("Mean and Standard Deviation of Difference")
print(mean(misclass.store[,1]-misclass.store[,iterations]))
print(sqrt(var(misclass.store[,1]-misclass.store[,iterations])))

print("Percent of Postive Differences")
print(sum(1*(misclass.store[,1]-misclass.store[,iterations])>0)/repeat.times)