    Gain insights into building and optimizing neural networks in Python. Delve into fundamental concepts, mathematical explanations, and practical implementations to enhance your machine learning skills.

Make your own neutral network in python final.png

Machine learning is one of the fastest growing fields, and we cannot emphasize enough about its importance. This course aims to teach one of the fundamental concepts of machine learning, i.e., Neural Network. You will learn the basic concepts of building a model as well as the mathematical explanation behind Neural Network and based on that; you will build one from scratch (in Python). You will also learn how to train and optimize your network to achieve a better result.

Make Your Own Neural Network in Python

## Calculate an error
Let's look at the first training example: the width is $3.0$ and the length is $1.0$ for a ladybug. If we tested the $y = Ax$ function with this example, where $x$ is $3.0$, we would get:

$$
y = (0.25) \times (3.0) = 0.75
$$

The function with the parameter $A$, which is set to the randomly chosen value of $0.25$, is suggesting that for a bug of width $3.0$, the length should be $0.75$. We know that's too small because the training data example tells us it must be a length of $1.0$. So, we have a difference, which indicates an error. Like before, with the miles to kilometers predictor, we can use this error to inform how we adjust the parameter $A$.

But before we do that, let's think about what $y$ should be again. If $y$ is $1.0$, then the line goes right through the point where the ladybug sits at $(x,y) = (3.0, 1.0)$. It's a subtle distinction, but we don't actually want that. We want the line to go above that point. Why? Because we want all the ladybug points to be below the line, not on it. The line needs to be a divider between ladybugs and caterpillars, not a predictor of a bug's length given its width.

So, let's try to aim for $y = 1.1$ when $x = 3.0$. It's just incrementally above $1.0$. We could've chosen $1.2$ or even $1.3$, but we don't want a larger number like $10$ or $100$ because that would make it more likely that the line will go above both the ladybugs and caterpillars data points, resulting in a separator that isn't useful at all. So the desired target is $1.1$, and the error $E$ is:

$$
\text{Error = (desired
target $-$ actual output)}

$$

which is,

$$
E = 1.1 - 0.75 = 0.35
$$

Let’s pause and remind ourselves what the error, the desired target, and the calculated value mean visually.

# Calculate an error
Let's look at the first training example: the width is $3.0$ and the length is $1.0$ for a ladybug. If we tested the $y = Ax$ function with this example, where $x$ is $3.0$, we would get:

$$
y = (0.25) \times (3.0) = 0.75
$$

The function with the parameter $A$, which is set to the randomly chosen value of $0.25$, is suggesting that for a bug of width $3.0$, the length should be $0.75$. We know that's too small because the training data example tells us it must be a length of $1.0$. So, we have a difference, which indicates an error. Like before, with the miles to kilometers predictor, we can use this error to inform how we adjust the parameter $A$.

But before we do that, let's think about what $y$ should be again. If $y$ is $1.0$, then the line goes right through the point where the ladybug sits at $(x,y) = (3.0, 1.0)$. It's a subtle distinction, but we don't actually want that. We want the line to go above that point. Why? Because we want all the ladybug points to be below the line, not on it. The line needs to be a divider between ladybugs and caterpillars, not a predictor of a bug's length given its width.

So, let's try to aim for $y = 1.1$ when $x = 3.0$. It's just incrementally above $1.0$. We could've chosen $1.2$ or even $1.3$, but we don't want a larger number like $10$ or $100$ because that would make it more likely that the line will go above both the ladybugs and caterpillars data points, resulting in a separator that isn't useful at all. So the desired target is $1.1$, and the error $E$ is:

$$
\text{Error = (desired
target $-$ actual output)}

$$

which is,

$$
E = 1.1 - 0.75 = 0.35
$$

Let’s pause and remind ourselves what the error, the desired target, and the calculated value mean visually.

Learn to calculate an error in the training classifier and the relationship between our parameter A and the error E.

Prologue

A Little Background

Let's Get Started!

Backward Propagation of Error

Adjusting the Link Weights

A Gentle Start with Python

Neural Network with Python

Testing Neural Network against MNIST Dataset

Some Suggested Improvements

Even More Fun!

Epilogue

Appendix: A Small Guide to Calculus

Errors in the Training Classifier

Calculate an error