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matlablinear-regressiongradient-descent

Linear Regression Code

I am taking Andrew Ng class on Machine Learning and implementing linear regression algorithm.

What is wrong with my code? 

function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
m = length(y); 
J_history = zeros(num_iters, 1);
h = (X*theta)
for iter = 1:num_iters
    theta(1,1) = theta(1,1)-(alpha/m)*sum((h-y).*X(:,1));
    theta(2,1) = theta(2,1)-(alpha/m)*sum((h-y).*X(:,2));  
    J_history(iter) = computeCost(X, y, theta);
end
end

Cost Function is given as:

function J = computeCost(X, y, theta)
m = length(y); 
h = (X*theta)
J = (1/(2*m))*sum((h-y).^2)
end

The value of J_history keeps increasing. It is giving very abnormal (large value) i.e. about 1000 times more than it should.

image

Solution

  • You need to update h and theta in the for loop as below

    function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
m = length(y); 
J_history = zeros(num_iters, 1);

for iter = 1:num_iters
    h = ((X*theta)-y)'*X;
    theta = theta - alpha*(1/m)*h';
    J_history(iter) = computeCost(X, y, theta);
end
end