The method we've just seen of calculating gradient descent is often called batch gradient descent, because each update to the coefficients happens inside an iteration over all the data in a single batch. With very large amounts of data, each iteration can be time-consuming and waiting for convergence could take a very long time.

An alternative method of gradient descent is called stochastic gradient descent or SGD. In this method, the estimates of the coefficients are continually updated as the input data is processed. The update method for stochastic gradient descent looks like this:

In fact, this is identical to batch gradient descent. The difference in application is purely that expression is calculated over a mini-batch—a random smaller subset of the overall data. The mini-batch size should be large enough to represent a fair sample of the input records—for our data, a reasonable mini-batch size might be about 250.

Stochastic gradient descent arrives at the...