Effects Chain Guide
Effects Chain Analysis

Neural networks provide a vast array of functionality in the realm of statistical modeling, from data transformation to classification and regression. Unfortunately, due to the computational complexity and generally large magnitude of data involved, the training of so called deep learning models has been historically relegated to only those with considerable computing resources. However with the advancement of GPU computing, and now a large number of easy-to-use frameworks, training such networks is fully accessible to anybody with a simple knowledge of Python and a personal computer. In this post we’ll go through the process of training your first neural network in Python using an exceptionally readable framework called Chainer. You can follow along this post through the tutorial here or via the Jupyter Notebook.

We’ll start by making one of the simplest neural networks possible, a linear regression. Then we’ll move into more complex territory by training a model to classify the MNIST hand written digits dataset (a standard benchmark for deep learning models).

Should you wish to execute the code examples below, you will need to install Chainer, Matplotlib, and NumPy. These are easily installed through the Python package manager, pip.

A flexible framework of neural networks for deep learning - chainer/chainer.

Effects Chain Guide

Make sure to upgrade your version of Cython if you have previously installed it or have it installed via Anaconda. If you don’t do this you may receive a cryptic error during the Chainer installation process.

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Be wary of enemy Muldrotha, the Gravetide s, though, as they may be able to recover from these effects more easily than you. Chainer’s haste is what opens the doors to some great synergies, though. Etali, Primal Storm, Grave Titan, Inferno Titan, or any creature with a powerful attack trigger is a great creature to reanimate.

If you have Jupyter installed, then you can just download the notebook structured around this post and run it on your local machine. First clone the stitchfix/Algorithms-Notebooks repository on GitHub and the notebook will be contained in the chainer-blog folder.

Effects Chain Analysis

To start, we will begin with a discussion of the three basic objects in Chainer, the chainer.Function, chainer.Optimizer and the chainer.Variable.

First we need to import a few things, which will be used throughout the notebook, including Matplotlib, NumPy, and some Chainer specific modules we will cover as we go.

Examining Chainer Variables and Functions

Let’s begin by making two Chainer variables, which are just wrapped NumPy arrays, named a and b. We’ll make them one value arrays, so that we can do some scalar operations with them.

In Chainer, Variable objects are both part symbolic and part numeric. They contain values in the data attribute, but also information about the chain of operations that has been performed on them. This history is extremely useful when trying to train neural networks because by calling the backward() method on a variable we can perform backpropagation or (reverse-mode) auto-differentiation, which provides our chosen optimizer with all the information needed to successfully update the weights of our neural networks.

This process can happen, because Chainer variables store the sequence of Chainer functions that act upon them and each function contains an analytic expression of its derivative. Some functions you will use will be parametric and contained in chainer.links (imported here as L). These types of functions are the ones whose parameters will be updated with each training iteration of our network. Other functions will be non-parametric, contained in chainer.functions (imported here as F), and merely perform a predefined mathematical operation on a variable. Even the addition and subtraction operations are promoted to Chainer functions and the history of operations of each variable is stored as part of the variable itself. This allows us to calculate derivatives of any variable with respect to any another.

Let’s see how this works by example. Below we will:

Inspect the value of our previously defined variables above by using the data attribute.
Backpropagate using the backward() method on the third variable, c.
Inspect the derivatives of the variables stored in the grad attribute.

Now that we know a little bit about the basics of what Chainer is doing, let’s use it to train the most basic possible neural network, a linear regression network. Of course the solution to the least squares optimization involved here can be calculated analytically via the normal equations much more efficiently, but this process will demonstrate the basic components of each network you’ll train going forward.

This network has no hidden units and involves just one input node, one output node, and a linear function linking the two of them.

To train our regression we will go through the following steps:

Generate random linearly dependent datasets.
Construct a function to perform a forward pass through the network with a Chainer Link.
Make a function to do the network training.

In general, the structure you’ll want to keep common to all neural networks that you make in Chainer involves making a forward function, which takes in your different parametric link functions and runs the data through them all in sequence.

Then writing a train function, which runs that forward pass over your batches of data for a number of full passes through the data called epochs, and then after each forward pass calculates a specified loss/objective function and updates the weights of the network using an optimizer and the gradients calculated through the backward method.

At the start Chainer practitioners often define the structure they’ll be working with by specifying the Link layers (here we’ll only need one). Then they will specify an optimizer to use, by instantiating one of the optimizer classes. Finally, they’ll tell the optimizer to keep track of and update the parameters of the specified model layers by calling the setup method on the optimizer instance with the layer to be tracked as an argument.

Plot Results During Training

The code below will train the model for 5 epochs at a time and plot the line which is given by the current network parameters in the linear link. You can see how the model converges to the correct solution as the line starts out as light blue and moves toward its magenta final state.

BONUS POINTS

If you’ve been following along doing your own code executions, try turning the above linear regression into a logistic regression. Use the following binary dataset for your dependent variable.

HINT

You’ll want to make use of the F.sigmoid() and F.sigmoid_cross_entropy() functions.

For this third and final part we will use the MNIST handwritten digit dataset and try to classify the correct numerical value written in a (28times28) pixel image. This is a classic benchmark for supervised deep learning architectures.

For this problem we will alter our simple linear regressors by now including some hidden linear neural network layers as well as introducing some non-linearity through the use of a non-linear activation function. This type of architecture is called a Multilayer Perceptron (MLP), and has been around for quite some time. Let’s see how it performs on the task at hand.

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Effect Chainer