You might be wondering why we went through all of this theory just to implement a simple multi-layer artificial network that can classify handwritten digits instead of using an open source Python machine learning library. One reason is that at the time of writing this book, scikit-learn does not have an MLP implementation. More importantly, we (machine learning practitioners) should have at least a basic understanding of the algorithms that we are using in order to apply machine learning techniques appropriately and successfully.

Now that we know how feedforward neural networks work, we are ready to explore more sophisticated Python libraries built on top of NumPy such as Theano http://deeplearning.net/software/theano/), which allows us to construct neural networks more efficiently. We will see this in Chapter 13, Parallelizing Neural Network Training with Theano. Over the last couple of years, Theano has gained a lot of popularity among machine learning researchers, who use it to construct deep neural networks because of its ability to optimize mathematical expressions for computations on multi-dimensional arrays utilizing Graphical Processing Units (GPUs).

A great collection of Theano tutorials can be found at http://deeplearning.net/software/theano/tutorial/index.html#tutorial.

There are also a number of interesting libraries that are being actively developed to train neural networks in Theano, which you should keep on your radar: