gradient descent seems to fail

Question

I implemented a gradient descent algorithm to minimize a cost function in order to gain a hypothesis for determining whether an image has a good quality. I did that in Octav

Answer 1

I think that your computeCost function is wrong. I attended NG's class last year and I have the following implementation (vectorized):

m = length(y);
J = 0;
predictions = X * theta;
sqrErrors = (predictions-y).^2;

J = 1/(2*m) * sum(sqrErrors);

The rest of the implementation seems fine to me, although you could also vectorize them.

theta_1 = theta(1) - alpha * (1/m) * sum((X*theta-y).*X(:,1));
theta_2 = theta(2) - alpha * (1/m) * sum((X*theta-y).*X(:,2));

Afterwards you are setting the temporary thetas (here called theta_1 and theta_2) correctly back to the "real" theta.

Generally it is more useful to vectorize instead of loops, it is less annoying to read and to debug.