How to build a Neural Network from scratch in Python

How to build a Neural Network from scratch in Python

In this article we will get into some of the details of building a neural network by Python. And understanding the inner workings of Deep Learning

What’s a Neural Network?

Neural Networks are like the workhorses of Deep learning. With enough data and computational power, they can be used to solve most of the problems in deep learning. It is very easy to use a Python or R library to create a neural network and train it on any dataset and get a great accuracy.

Most introductory texts to Neural Networks brings up brain analogies when describing them. Without delving into brain analogies, I find it easier to simply describe Neural Networks as a mathematical function that maps a given input to a desired output.

Neural Networks consist of the following components

  • An input layer, x
  • An arbitrary amount of hidden layers
  • An output layer, ŷ
  • A set of weights and biases between each layer, W and b
  • A choice of activation function for each hidden layer, σ. In this tutorial, we’ll use a Sigmoid activation function.

The diagram below shows the architecture of a 2-layer Neural Network (note that the input layer is typically excluded when counting the number of layers in a Neural Network)

Architecture of a 2-layer Neural Network

Creating a Neural Network class in Python is easy.

class NeuralNetwork:
    def __init__(self, x, y):
        self.input      = x
        self.weights1   = np.random.rand(self.input.shape[1],4) 
        self.weights2   = np.random.rand(4,1)                 
        self.y          = y
        self.output     = np.zeros(y.shape)

Training the Neural Network

The output ŷ of a simple 2-layer Neural Network is:

You might notice that in the equation above, the weights W and the biases b are the only variables that affects the output ŷ.

Naturally, the right values for the weights and biases determines the strength of the predictions. The process of fine-tuning the weights and biases from the input data is known as training the Neural Network.

Each iteration of the training process consists of the following steps:

  • Calculating the predicted output ŷ, known as feedforward
  • Updating the weights and biases, known as backpropagation

The sequential graph below illustrates the process.

Feedforward

As we’ve seen in the sequential graph above, feedforward is just simple calculus and for a basic 2-layer neural network, the output of the Neural Network is:

Let’s add a feedforward function in our python code to do exactly that. Note that for simplicity, we have assumed the biases to be 0.

class NeuralNetwork:
    def __init__(self, x, y):
        self.input      = x
        self.weights1   = np.random.rand(self.input.shape[1],4) 
        self.weights2   = np.random.rand(4,1)                 
        self.y          = y
        self.output     = np.zeros(self.y.shape)

    def feedforward(self):
        self.layer1 = sigmoid(np.dot(self.input, self.weights1))
        self.output = sigmoid(np.dot(self.layer1, self.weights2))

However, we still need a way to evaluate the “goodness” of our predictions (i.e. how far off are our predictions)? The Loss Function allows us to do exactly that.

Loss Function

There are many available loss functions, and the nature of our problem should dictate our choice of loss function. In this tutorial, we’ll use a simple sum-of-sqaures error as our loss function.

That is, the sum-of-squares error is simply the sum of the difference between each predicted value and the actual value. The difference is squared so that we measure the absolute value of the difference.

Our goal in training is to find the best set of weights and biases that minimizes the loss function.

Backpropagation

Now that we’ve measured the error of our prediction (loss), we need to find a way to propagate the error back, and to update our weights and biases.

In order to know the appropriate amount to adjust the weights and biases by, we need to know the derivative of the loss function with respect to the weights and biases.

Recall from calculus that the derivative of a function is simply the slope of the function.


Gradient descent algorithm

If we have the derivative, we can simply update the weights and biases by increasing/reducing with it(refer to the diagram above). This is known as gradient descent.

However, we can’t directly calculate the derivative of the loss function with respect to the weights and biases because the equation of the loss function does not contain the weights and biases. Therefore, we need the chain rule to help us calculate it.


Chain rule for calculating derivative of the loss function with respect to the weights. Note that for simplicity, we have only displayed the partial derivative assuming a 1-layer Neural Network.

Phew! That was ugly but it allows us to get what we needed — the derivative (slope) of the loss function with respect to the weights, so that we can adjust the weights accordingly.

Now that we have that, let’s add the backpropagation function into our python code.

class NeuralNetwork:
    def __init__(self, x, y):
        self.input      = x
        self.weights1   = np.random.rand(self.input.shape[1],4) 
        self.weights2   = np.random.rand(4,1)                 
        self.y          = y
        self.output     = np.zeros(self.y.shape)

    def feedforward(self):
        self.layer1 = sigmoid(np.dot(self.input, self.weights1))
        self.output = sigmoid(np.dot(self.layer1, self.weights2))

    def backprop(self):
        # application of the chain rule to find derivative of the loss function with respect to weights2 and weights1
        d_weights2 = np.dot(self.layer1.T, (2*(self.y - self.output) * sigmoid_derivative(self.output)))
        d_weights1 = np.dot(self.input.T,  (np.dot(2*(self.y - self.output) * sigmoid_derivative(self.output), self.weights2.T) * sigmoid_derivative(self.layer1)))

        # update the weights with the derivative (slope) of the loss function
        self.weights1 += d_weights1
        self.weights2 += d_weights2

For a deeper understanding of the application of calculus and the chain rule in backpropagation, I strongly recommend this tutorial by 3Blue1Brown.

Putting it all together

Now that we have our complete python code for doing feedforward and backpropagation, let’s apply our Neural Network on an example and see how well it does.

Our Neural Network should learn the ideal set of weights to represent this function. Note that it isn’t exactly trivial for us to work out the weights just by inspection alone.

Let’s train the Neural Network for 1500 iterations and see what happens. Looking at the loss per iteration graph below, we can clearly see the loss monotonically decreasing towards a minimum. This is consistent with the gradient descent algorithm that we’ve discussed earlier.

Let’s look at the final prediction (output) from the Neural Network after 1500 iterations.


Predictions after 1500 training iterations

We did it! Our feedforward and backpropagation algorithm trained the Neural Network successfully and the predictions converged on the true values.

Note that there’s a slight difference between the predictions and the actual values. This is desirable, as it prevents overfitting and allows the Neural Network to generalize better to unseen data.

What’s Next?

Fortunately for us, our journey isn’t over. There’s still much to learn about Neural Networks and Deep Learning. For example:

  • What other activation function can we use besides the Sigmoid function?
  • Using a learning rate when training the Neural Network
  • Using convolutions for image classification tasks

I’ll be writing more on these topics soon, so do follow me on Medium and keep and eye out for them!

Final Thoughts

I’ve certainly learnt a lot writing my own Neural Network from scratch.

Although Deep Learning libraries such as TensorFlow and Keras makes it easy to build deep nets without fully understanding the inner workings of a Neural Network, I find that it’s beneficial for aspiring data scientist to gain a deeper understanding of Neural Networks.

This exercise has been a great investment of my time, and I hope that it’ll be useful for you as well!

How to get started with Python for Deep Learning and Data Science

How to get started with Python for Deep Learning and Data Science

A step-by-step guide to setting up Python for Deep Learning and Data Science for a complete beginner

A step-by-step guide to setting up Python for Deep Learning and Data Science for a complete beginner

You can code your own Data Science or Deep Learning project in just a couple of lines of code these days. This is not an exaggeration; many programmers out there have done the hard work of writing tons of code for us to use, so that all we need to do is plug-and-play rather than write code from scratch.

You may have seen some of this code on Data Science / Deep Learning blog posts. Perhaps you might have thought: “Well, if it’s really that easy, then why don’t I try it out myself?”

If you’re a beginner to Python and you want to embark on this journey, then this post will guide you through your first steps. A common complaint I hear from complete beginners is that it’s pretty difficult to set up Python. How do we get everything started in the first place so that we can plug-and-play Data Science or Deep Learning code?

This post will guide you through in a step-by-step manner how to set up Python for your Data Science and Deep Learning projects. We will:

  • Set up Anaconda and Jupyter Notebook
  • Create Anaconda environments and install packages (code that others have written to make our lives tremendously easy) like tensorflow, keras, pandas, scikit-learn and matplotlib.

Once you’ve set up the above, you can build your first neural network to predict house prices in this tutorial here:

Build your first Neural Network to predict house prices with Keras

Setting up Anaconda and Jupyter Notebook

The main programming language we are going to use is called Python, which is the most common programming language used by Deep Learning practitioners.

The first step is to download Anaconda, which you can think of as a platform for you to use Python “out of the box”.

Visit this page: https://www.anaconda.com/distribution/ and scroll down to see this:

This tutorial is written specifically for Windows users, but the instructions for users of other Operating Systems are not all that different. Be sure to click on “Windows” as your Operating System (or whatever OS that you are on) to make sure that you are downloading the correct version.

This tutorial will be using Python 3, so click the green Download button under “Python 3.7 version”. A pop up should appear for you to click “Save” into whatever directory you wish.

Once it has finished downloading, just go through the setup step by step as follows:

Click Next

Click “I Agree”

Click Next

Choose a destination folder and click Next

Click Install with the default options, and wait for a few moments as Anaconda installs

Click Skip as we will not be using Microsoft VSCode in our tutorials

Click Finish, and the installation is done!

Once the installation is done, go to your Start Menu and you should see some newly installed software:

You should see this on your start menu

Click on Anaconda Navigator, which is a one-stop hub to navigate the apps we need. You should see a front page like this:

Anaconda Navigator Home Screen

Click on ‘Launch’ under Jupyter Notebook, which is the second panel on my screen above. Jupyter Notebook allows us to run Python code interactively on the web browser, and it’s where we will be writing most of our code.

A browser window should open up with your directory listing. I’m going to create a folder on my Desktop called “Intuitive Deep Learning Tutorial”. If you navigate to the folder, your browser should look something like this:

Navigating to a folder called Intuitive Deep Learning Tutorial on my Desktop

On the top right, click on New and select “Python 3”:

Click on New and select Python 3

A new browser window should pop up like this.

Browser window pop-up

Congratulations — you’ve created your first Jupyter notebook! Now it’s time to write some code. Jupyter notebooks allow us to write snippets of code and then run those snippets without running the full program. This helps us perhaps look at any intermediate output from our program.

To begin, let’s write code that will display some words when we run it. This function is called print. Copy and paste the code below into the grey box on your Jupyter notebook:

print("Hello World!")

Your notebook should look like this:

Entering in code into our Jupyter Notebook

Now, press Alt-Enter on your keyboard to run that snippet of code:

Press Alt-Enter to run that snippet of code

You can see that Jupyter notebook has displayed the words “Hello World!” on the display panel below the code snippet! The number 1 has also filled in the square brackets, meaning that this is the first code snippet that we’ve run thus far. This will help us to track the order in which we have run our code snippets.

Instead of Alt-Enter, note that you can also click Run when the code snippet is highlighted:

Click Run on the panel

If you wish to create new grey blocks to write more snippets of code, you can do so under Insert.

Jupyter Notebook also allows you to write normal text instead of code. Click on the drop-down menu that currently says “Code” and select “Markdown”:

Now, our grey box that is tagged as markdown will not have square brackets beside it. If you write some text in this grey box now and press Alt-Enter, the text will render it as plain text like this:

If we write text in our grey box tagged as markdown, pressing Alt-Enter will render it as plain text.

There are some other features that you can explore. But now we’ve got Jupyter notebook set up for us to start writing some code!

Setting up Anaconda environment and installing packages

Now we’ve got our coding platform set up. But are we going to write Deep Learning code from scratch? That seems like an extremely difficult thing to do!

The good news is that many others have written code and made it available to us! With the contribution of others’ code, we can play around with Deep Learning models at a very high level without having to worry about implementing all of it from scratch. This makes it extremely easy for us to get started with coding Deep Learning models.

For this tutorial, we will be downloading five packages that Deep Learning practitioners commonly use:

  • Set up Anaconda and Jupyter Notebook
  • Create Anaconda environments and install packages (code that others have written to make our lives tremendously easy) like tensorflow, keras, pandas, scikit-learn and matplotlib.

The first thing we will do is to create a Python environment. An environment is like an isolated working copy of Python, so that whatever you do in your environment (such as installing new packages) will not affect other environments. It’s good practice to create an environment for your projects.

Click on Environments on the left panel and you should see a screen like this:

Anaconda environments

Click on the button “Create” at the bottom of the list. A pop-up like this should appear:

A pop-up like this should appear.

Name your environment and select Python 3.7 and then click Create. This might take a few moments.

Once that is done, your screen should look something like this:

Notice that we have created an environment ‘intuitive-deep-learning’. We can see what packages we have installed in this environment and their respective versions.

Now let’s install some packages we need into our environment!

The first two packages we will install are called Tensorflow and Keras, which help us plug-and-play code for Deep Learning.

On Anaconda Navigator, click on the drop down menu where it currently says “Installed” and select “Not Installed”:

A whole list of packages that you have not installed will appear like this:

Search for “tensorflow”, and click the checkbox for both “keras” and “tensorflow”. Then, click “Apply” on the bottom right of your screen:

A pop up should appear like this:

Click Apply and wait for a few moments. Once that’s done, we will have Keras and Tensorflow installed in our environment!

Using the same method, let’s install the packages ‘pandas’, ‘scikit-learn’ and ‘matplotlib’. These are common packages that data scientists use to process the data as well as to visualize nice graphs in Jupyter notebook.

This is what you should see on your Anaconda Navigator for each of the packages.

Pandas:

Installing pandas into your environment

Scikit-learn:

Installing scikit-learn into your environment

Matplotlib:

Installing matplotlib into your environment

Once it’s done, go back to “Home” on the left panel of Anaconda Navigator. You should see a screen like this, where it says “Applications on intuitive-deep-learning” at the top:

Now, we have to install Jupyter notebook in this environment. So click the green button “Install” under the Jupyter notebook logo. It will take a few moments (again). Once it’s done installing, the Jupyter notebook panel should look like this:

Click on Launch, and the Jupyter notebook app should open.

Create a notebook and type in these five snippets of code and click Alt-Enter. This code tells the notebook that we will be using the five packages that you installed with Anaconda Navigator earlier in the tutorial.

import tensorflow as tf

import keras

import pandas

import sklearn

import matplotlib

If there are no errors, then congratulations — you’ve got everything installed correctly:

A sign that everything works!

If you have had any trouble with any of the steps above, please feel free to comment below and I’ll help you out!

*Originally published by Joseph Lee Wei En at *medium.freecodecamp.org

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Deep Learning Tutorial with Python | Machine Learning with Neural Networks

Deep Learning Tutorial with Python | Machine Learning with Neural Networks

In this video, Deep Learning Tutorial with Python | Machine Learning with Neural Networks Explained, Frank Kane helps de-mystify the world of deep learning and artificial neural networks with Python!

Explore the full course on Udemy (special discount included in the link): http://learnstartup.net/p/BkS5nEmZg

In less than 3 hours, you can understand the theory behind modern artificial intelligence, and apply it with several hands-on examples. This is machine learning on steroids! Find out why everyone’s so excited about it and how it really works – and what modern AI can and cannot really do.

In this course, we will cover:

•    Deep Learning Pre-requistes (gradient descent, autodiff, softmax)

•    The History of Artificial Neural Networks

•    Deep Learning in the Tensorflow Playground

•    Deep Learning Details

•    Introducing Tensorflow

•    Using Tensorflow

•    Introducing Keras

•    Using Keras to Predict Political Parties

•    Convolutional Neural Networks (CNNs)

•    Using CNNs for Handwriting Recognition

•    Recurrent Neural Networks (RNNs)

•    Using a RNN for Sentiment Analysis

•    The Ethics of Deep Learning

•    Learning More about Deep Learning

At the end, you will have a final challenge to create your own deep learning / machine learning system to predict whether real mammogram results are benign or malignant, using your own artificial neural network you have learned to code from scratch with Python.

Separate the reality of modern AI from the hype – by learning about deep learning, well, deeply. You will need some familiarity with Python and linear algebra to follow along, but if you have that experience, you will find that neural networks are not as complicated as they sound. And how they actually work is quite elegant!

This is hands-on tutorial with real code you can download, study, and run yourself.

Thanks for reading

If you liked this post, share it with all of your programming buddies!

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