Before we get into measuring how well a machine learning model performs, let's clarify what we mean by a "model" in this context. You've already seen that evaluation is an essential step, but what exactly are we evaluating?

Think of a machine learning model as a specific type of computer program. Unlike traditional programs where developers write explicit, step-by-step instructions (if this, then do that), a machine learning model learns its own rules directly from data. It identifies patterns, trends, and relationships within the data it's trained on.

At its core, you can view a model as a mathematical function, let's call it $f$ . This function takes some input data, often called features, and produces an output.

Input (Features): These are the measurable characteristics or attributes of the thing you are interested in. For example, if you want to predict house prices, the features might be the square footage, number of bedrooms, and age of the house.
Model ( $f$ ): This is the learned function. It contains internal parameters or structures that were adjusted during a "training" process using example data. It encapsulates the patterns learned from that data.
Output (Prediction/Estimate): This is the result generated by the model when given new input features. It could be a category (like "spam" or "not spam") or a numerical value (like "$250,000").

A simplified view of a machine learning model taking input features and producing an output prediction.

Let's revisit the types of problems mentioned earlier:

Models in Classification

In a classification problem, the model learns to assign inputs to predefined categories or classes.

Example: An email spam detector.
- Input Features: Words in the email subject, sender's address, time sent.
- Model: Learns which combinations of features are typical for spam versus legitimate emails (often called "ham").
- Output: A category label, like spam or ham.

The model essentially learns a decision boundary to separate the different classes based on the input features.

Models in Regression

In a regression problem, the model learns to predict a continuous numerical value.

Example: Predicting the price of a used car.
- Input Features: Car's make, model, year, mileage, condition.
- Model: Learns the relationship between these features and the car's market value. This might resemble learning the parameters of an equation, like finding the slope ( $m$ ) and intercept ( $b$ ) in a simple linear relationship $y = mx + b$ .
- Output: A numerical value, like $15,200.

So, when we talk about evaluating a model, we're assessing how accurately and reliably this learned function $f$ produces the correct output (category or number) when it encounters new, previously unseen input data. The goal is to determine if the patterns the model learned from the training data generalize well to the real world.