Entering values into a linear regression / gradient descent algorithm

Question

The instructor of the machine learning course I've been taking whipped this algorithm at my head without explaining how to apply it to a training set.

m = number of training sets (3)
j = subscript 0 or 1
x(i) = x from the ith training set
y(i) = y from the ith training set
alpha = ?
h theta = ?

If I had a training set of (1,1), (2,2), (3,3), how would I go about entering it into this algorithm?

Answer 1

you do this with one training set at a time.so, x(i) = the "features" for the ith subject h_theta(x(i)) = the predicted response for the ith subject given the features x(i) y(i) = the actual response for the ith subject thats a cost function. alpha is the learning rate, you choose it. h_theta is the hypothesis function that describes your data (for example, h_theta(x) = theta_0 + theta_1*x).

basically you start with an initial guess of the theta's (theta_0 = 1, theta_1= 1), evaluate the expression "temp 1" above, and keep updating theta_{n+1} until theta_{n+1} - theta_{n} has a very small negligible difference (say, 10^-6).