Training an artificial neural network

Now that we have seen a neural network in action and have gained a basic understanding of how it works by looking over the code, let's dig a little bit deeper into some of the concepts, such as the logistic cost function and the backpropagation algorithm that we implemented to learn the weights.

Computing the logistic cost function

The logistic cost function that we implemented as the _get_cost method is actually pretty simple to follow since it is the same cost function that we described in the logistic regression section in Chapter 3, A Tour of Machine Learning Classifiers Using Scikit-learn.

Here, is the sigmoid activation of the th unit in one of the layers which we compute in the forward propagation step:

Now, let's add a regularization term, which allows us to reduce the degree of overfitting. As you will recall from earlier chapters, the L2 and L1 regularization terms are defined as follows (remember that we don't regularize the bias units):

Although...