simple regression using batch gradient descent

simple_regression_batch_gradient_descent

def target_fn(theta):
    """want to minimize squared errors as a function of *theta*, so we hardcode in the data"""
    alpha, beta = theta
    return sum_of_squared_errors(alpha, beta, num_friends_good, daily_minutes_good)
                       
def gradient_fn(theta):
    """similarly, need gradient as a function of *theta*, so hardcode in the data"""
    alpha, beta = theta
    result = [0, 0]
    for x_i, y_i in zip(num_friends_good, daily_minutes_good):
        e = error(alpha, beta, x_i, y_i)
        result[0] += -2 * e
        result[1] += -2 * e * x_i
        
    return result

theta = [random.random(), random.random()]
    
alpha, beta = minimize_batch(target_fn, gradient_fn, theta, 1.0)
print "alpha", alpha
print "beta", beta