Get started with the core components of machine learning and learn to create supervised learning systems.

Zero to Hero in Python for Machine Learning

This module is a comprehensive introduction to the core components of machine learning for software engineers. We’ll be introduced to the most relevant components of the machine learning discipline. We’ll also cover the differences between traditional programming and machine learning through hands-on development in supervised learning. By the end of this module, we’ll have a working knowledge of modern techniques in the field of machine learning.

Fundamentals of Machine Learning

# Background
Let’s look for a better `train()` algorithm. The job of `train()` is to find the parameters that minimize the loss, so let’s start by focusing on `loss()` itself:

```python
def loss(X, Y, w, b):
  return np.average((predict(X, w, b) - Y) ** 2)
```
Look at this function’s arguments. The $X$ and $Y$ contain the input variables and the labels, so they never change from one call of `loss()` to the next. To make the discussion simple, let’s also temporarily fix $b$ at $0$. So now the only variable is $w$.

How does the loss change as w changes? We put together a program that plots loss()` for w ranging from $-1$ to $4$, and draws a green cross on its minimum value. Let’s look at the following graph:

Let’s call it the loss curve. The entire idea of `train()` is to find that marked spot at the bottom of the curve. It is the value of $w$ that gives the minimum loss. At $w$, the model approximates the data points as well as it can.

Now imagine that the loss curve is a valley, and there is a hiker standing somewhere in this valley. The hiker wants to reach their basecamp, right where the marked spot is—but it’s dark, and they can only see the terrain right around her feet. To find the basecamp, they can follow a simple approach. They can walk in the direction of the steepest downward slope. If the terrain does not contain holes or cliffs and our loss function does not—then each step will take the hiker closer to the basecamp.

To convert that idea into running code, we need to measure the slope of the loss curve. In mathspeak, that slope is called the gradient of the curve. By convention, the gradient at a certain point is an arrow that points directly uphill from that point, like this:

To measure the gradient, we can use a mathematical tool called the derivative of the loss with respect to the weight,  that is written as $\frac{\partial L}{\partial w}$ More formally, the derivative at a certain point measures how the loss $L$ changes at that point for small variations of $w$. Imagine if we increase the weight just a little bit, what will happen to the loss?


In the case of the diagram here, the derivative would be a negative number, meaning that the loss decreases when $w$ increases. If the hiker were standing on the right side of the diagram, the derivative would be positive, meaning that the loss increases when $w$ increases. At the minimum point of the curve, (the point marked with the cross) the curve is level, and the derivative is zero.

Note that the hiker would have to walk in the direction opposite to the gradient to approach the minimum. So, in the case of a negative derivative like the one in the picture, they would take a step in the positive direction. The size of the hiker’s steps should also be proportional to the derivative. If the derivative is a big number (either positive or negative), this means the curve is steep, and the basecamp is far away. So the hiker can take big steps with confidence. As they approach the basecamp, the derivative becomes smaller, and so do their steps.

The algorithm described above is called **gradient descent** or GD for short. Implementing it requires a tiny bit of math.

# The math behind gradient descent

Let’s discuss how to crack gradient descent with math. First, let’s rewrite the mean squared error loss in mathematical notation:


Discover the math behind gradient descent to deepen our understanding by exploring graphical representations.

Gradient Descent

Background