GDForOneDim

GDForOneDim.R

#Generate one dimensional data
X<-sample(x=1:100,size=20)
#Simulate labels
Y<-sample(x=c(-1,1),size=20,replace=TRUE)
#Here's how my data looks
data<-as.matrix(cbind(X,Y))
#I am going to use squared loss i.e. Loss=(y - h(x))^2 where h(x)=WX 
#You could also do a slight variant where you have
#a bias term in the hypothesis i.e. h(x)=WX+b
#Estimate the gradient as follows
grad<-function(x,y,w)
{
 gradientPt<--2*x*(y-x*w)
 gradient<-sum(gradientPt)
 return(gradient)
}
#Perform the descent
grad.descent<-function(X,Y,W,maxitr)
{	
#Set the number of examples
nEG<-nrow(as.matrix(X))	
#Set the alpha parameter
alpha=0.5
#Set the number of iterations 
for (i in 1:maxitr)
{
 W <- W-(alpha*grad(X,Y,W))/nEG
 print(W)
}
return(W)

}
#Define the hypothesis
h<-function(X,W)
{return (X*W)}
#Find the loss
Loss<-matrix(data=0,nrow=20,ncol=1)
W<-grad.descent(X,Y,1,10)
for(j in 1:20)
{
 Loss[j]<-(Y[j]-h(X[j],W))^2
}
# Find the mean of the Squared Loss
mean(Loss)