Chapter 5: Defining the Model

Welcome to Chapter 5! In this chapter, we will define our model, a simple linear function, and explain how it uses the inputs and weights to produce outputs. We will start by describing our simple linear model and why it's an ideal starting point for learning. We will then explain how inputs and weights interact within the model to produce outputs. Finally, we will walk through the Python code that defines our model, explaining each line in detail.

5.1: Linear Model: A Simplified Neural Network

In the world of machine learning, a model is a mathematical representation of a real-world process. For our purposes, we are going to use a simple linear model. This model is a simplified version of a neural network, making it an ideal starting point for beginners.

A linear model is like a recipe. It takes inputs (the ingredients), processes them using weights (the cooking instructions), and produces an output (the finished dish). The weights are the key part of the recipe that we need to get right. If we use the right weights, our recipe will produce a delicious dish (accurate predictions). If we use the wrong weights, our dish might not turn out so well (inaccurate predictions).

5.2: How the Model Works: Inputs, Weights and Outputs

Our model works by taking an input, multiplying it by a weight, and producing an output. This is similar to how a chef might use a recipe. The chef takes an ingredient (input), processes it according to the recipe (weight), and produces a dish (output).

In our case, the input is a number, the weight is another number, and the output is the result of multiplying the input by the weight. This is a simple process, but it's the foundation of how more complex neural networks work.

Let's consider an example. Suppose our input is 2 and our weight is 3. Our model would multiply the input by the weight to produce an output of 6. If our weight was 4 instead of 3, our output would be 8. As you can see, the weight determines how much the input influences the output.

5.3: Code Explanation: Model Function Definition

Now, let's go through the Python code that defines our model. We'll explain each line to ensure you understand how the code implements the concepts we've discussed.

def model(X, weights):
    return np.dot(X, weights)

This code defines a function called model that takes two arguments: X and weights. X is the input to our model, and weights are the weights our model uses to process the input.

The function returns the result of the dot product of X and weights. The dot product is a mathematical operation that multiplies corresponding elements of two arrays and sums the results. In our case, since X and weights are both one-dimensional arrays (or vectors), the dot product is equivalent to multiplying the input by the weight.

That's it for this chapter! You now understand how our simple linear model works and how to define it in Python. In the next chapter, we will introduce the concept of a loss function, which measures how accurate our model's predictions are. Stay tuned!