Gradient descent Search implemented in matlab theta1 incorrect

Question

I studied the Machine learning course taught by Prof. Andrew Ng. This is the link

I try to implement the 1st assignment of this course. Exercise 2: Linear Regression based upon Supervised learning problem

1.Implement gradient descent using a learning rate of alpha=0.07.Since Matlab/Octave and Octave index vectors starting from 1 rather than 0, you'll probably use theta(1) and theta(2) in Matlab/Octave to represent theta0 and theta1.

I write down a matlab code to solve this problem:

clc
clear
close all

x = load('ex2x.dat');
y = load('ex2y.dat');
figure % open a new figure window
 plot(x, y, '*');
 ylabel('Height in meters')
 xlabel('Age in years')
m = length(y); % store the number of training examples
x = [ones(m, 1), x]; % Add a column of ones to x
theta = [0 0];
temp=0,temp2=0;
h=[];
alpha=0.07;n=2; %alpha=learning rate
for i=1:m
temp1=0;
for j=1:n
    h(j)=theta(j)*x(i,j);
    temp1=temp1+h(j);
end
temp=temp+(temp1-y(i));
temp2=temp2+((temp1-y(i))*(x(i,1)+x(i,2)));

end
theta(1)=theta(1)-(alpha*(1/m)*temp);
theta(2)=theta(2)-(alpha*(1/m)*temp2);

I get the answer :

>> theta

theta =

0.0745    0.4545

Here, 0.0745 is exact answer but 2nd one is not accurate.

Actual answer

theta =

0.0745 0.3800

The data set is provided in the link. Can any one help me to fix the problem?

Mendi Barel Mendi Barel · Accepted Answer · 2018-10-18T04:25:18

You get wrong results because you write long unnecessary code that is easily prone to bugs, that is exactly why we have matlab:

clear

x = load('d:/ex2x.dat');
y = load('d:/ex2y.dat');
figure(1), clf, plot(x, y, '*'), xlabel('Age in years'), ylabel('Height in meters')

m = length(y); % store the number of training examples
x = [ones(m, 1), x]; % Add a column of ones to x


theta=[0,0];  alpha=0.07;

residuals = x*theta' - y ; %same as:  sum(x.*theta,2)-y
theta = theta - alpha*mean(residuals.*x);

disp(theta)

Gradient descent Search implemented in matlab theta1 incorrect

1 Answers