LogisticRegressionNewtom.R

#-------------------Retrieving and Cleaning Data--------------
data = read.csv("filter.csv",header=T, na.strings=c(""))
sapply(data, function(x) sum(is.na(x)))
data = subset(data,select=c(2,3,5,6,7,8,10,12))
data$Age[is.na(data$Age)] = mean(data$Age, na.rm = T)
#is.factor(data$Sex)
#is.factor(data$Embarked)
data = data[!is.na(data$Embarked),]
rownames(data) = NULL
trainData = data[1:800,]
testData = data[801:889,]

#-----------------It starts----------------------------------

#simod 
g = function(z){
  return (1/(1+exp(-z)))
}

#Hypothesis
h = function(x, th){
  return (g(x%*%th))
}

#cost
J = function(x, y, th, m){
  return( 1/m * sum(-y * log(h(x,th)) - (1 - y) * log(1 - h(x,th))) )
}

# derivative of J (gradient)
grad = function (x,y,th,m) {
  return( 1/m * t(x) %*% (h(x,th) - y))
} # grad(x,y,th,m)

# Hessian
H = function (x,y,th,m) {
  return (1/m * t(x) %*% x * diag(h(x,th)) * diag(1 - h(x,th)))
} # H(x,y,th,m)

#setup

j = array(0, c(10, 1))
m = length (trainData$Sex)
x = matrix(c(rep(1, m), trainData$Pclass, trainData$Sex, trainData$Age, trainData$SibSp, trainData$Parch, trainData$Fare, trainData$Embarked),
            ncol =8)
y = matrix(trainData$Survived, ncol = 1)
th = matrix(0,8)

for( i in 1:10){
  j[i] = J(x,y,th,m)
  th = th - solve(H(x,y,th,m)) %*% grad(x,y,th,m) 
}
print (th)
plot(j, xlab="iterations", ylab="cost J")

test = testData[3,]
test3 = rapply(test, c)
test2 = c(1,2,3,4,5,6,7,8)
ans = g(test3%*%th)[1,1]
ans2 = g(c(1,1,1,11,1,2,120,0)%*%th)
print(ans)
print (ans2)

correct = 0
trueTrue = 0
trueFalse = 0
falseTrue = 0
falseFalse = 0

for (i in 1:80){
  test = testData[i,]
  test3 = rapply(test, c)
  test3[1] = 1
  ans = g(test3%*%th)[1,1]
  if(ans < 0.4)
    ans = 0
  if (ans >= 0.4)
    ans = 1
  final  = 0
  
  if (ans == testData[i,]$Survived){
    final = 1
    if(ans == 0)
      falseFalse = falseFalse+1
    if (ans == 1)
      trueTrue = trueTrue + 1
  }
  if(ans != testData[i,]$Survived){
    if(ans == 1)
      trueFalse = trueFalse + 1
    if(ans == 0)
      falseTrue = falseTrue + 1
  }
  #tmp = c(ans, testData[i,]$Survived)
  print (final)
  correct = correct + final

}


#---------------------------Summary--------------------------------
print (correct)
print ("True True")
print (trueTrue)
print ("True False")
print (trueFalse)
print ("False True")
print (falseTrue)
print ("False False")
print (falseFalse)