Supervised vs. unsupervised and regression vs. classification

Welcome to the Basics of Statistical Learning!

Welcome, future actuaries! As you dive into Exam SRM, you'll find that Statistical Learning is the heart of modern data analysis. Think of this chapter as your "GPS" for the rest of the exam. Before we can build complex models to predict insurance claims or stock prices, we need to know exactly what kind of problem we are trying to solve.

In this section, we will learn how to categorize every model into two main "styles" (Supervised vs. Unsupervised) and two main "goals" (Regression vs. Classification). Don't worry if these terms sound fancy; by the end of these notes, they will feel like second nature!

1. Supervised vs. Unsupervised Learning

The biggest distinction in statistical learning is whether we have a "teacher" guiding our model or if the model has to figure things out on its own.

Supervised Learning: Learning with a Teacher

In Supervised Learning, for every observation of input data \( (x_i) \), we have a corresponding output or "label" \( (y_i) \). Our goal is to find a function that maps the inputs to the output so accurately that when we see new inputs, we can predict the new output.

Analogy: Imagine you are teaching a child to identify fruit. You show them an apple and say, "This is an apple." You show them an orange and say, "This is an orange." Because you provided the "answers" (the labels), this is supervised learning.

Actuarial Example: Predicting the cost of a claim (the output \( Y \)) based on the age of the driver and the type of car (the inputs \( X \)). We use past data where we already know how much the claims cost to "supervise" the model.

Unsupervised Learning: Learning by Discovery

In Unsupervised Learning, we have inputs \( (x_i) \), but no corresponding output \( (y_i) \). There is no "answer key" and no "teacher." The goal is to find interesting patterns, structures, or groupings within the data.

Analogy: Imagine giving that same child a giant bucket of random blocks of different shapes and colors but saying nothing. The child might start putting all the round blocks in one pile and the square blocks in another. They aren't "naming" them; they are just finding patterns based on similarities.

Actuarial Example: Market Segmentation. You have data on thousands of policyholders. You don't have a specific thing to predict, but you want to see if they naturally fall into groups (e.g., "Young urban professionals" vs. "Retired rural homeowners") to better target your marketing.

Quick Review: The Main Difference

• Supervised: We have \( X \) and \( Y \). We want to predict \( Y \).
• Unsupervised: We only have \( X \). We want to find patterns in \( X \).

2. Regression vs. Classification

If you are doing Supervised Learning (meaning you have an output \( Y \)), your next step is to decide if you are dealing with a Regression problem or a Classification problem. This depends entirely on the type of output variable you have.

Regression: Predicting Numbers

We use Regression when the response variable \( Y \) is quantitative (numerical). These are variables where the numbers have mathematical meaning and can be ordered.

Key Term: Quantitative variables take on numerical values (e.g., $100, 55.5 years old, 12 inches).

Examples:
\n• Predicting the price of a stock.
\n• Estimating the time until a piece of equipment fails.
\n• Calculating the total loss from a hurricane.

Classification: Predicting Categories

We use Classification when the response variable \( Y \) is qualitative (categorical). These represent "classes" or "labels" rather than measurements.

Key Term: Qualitative variables take on values in one of \( K \) different classes (e.g., Yes/No, Blue/Green/Red, Pass/Fail).

Examples:
\n• Will a policyholder renew their policy? (Yes or No).
\n• Is a credit card transaction fraudulent or legitimate?
\n• Assigning a credit rating (A, B, C, or D).

Memory Aid: The "C" Trick

• Classification is for Categories (labels like "Group A" or "Group B").
\n• Regression is for Real numbers (measurements like $5.50 or 100 degrees).

3. Important Nuances and Common Mistakes

Don't worry if the line feels blurry sometimes! Here are a few things that often trip students up:

The "Logistic Regression" Confusion

Warning! There is a technique called Logistic Regression. Even though it has the word "Regression" in its name, it is almost always used for Classification. It estimates the probability that an observation belongs to a category (like the probability that a person will die during a policy term).

Can we treat numbers as categories?

Sometimes, we treat a numerical variable as a category. For example, if we are predicting a star rating (1, 2, 3, 4, or 5), we could treat it as regression (since 5 is better than 4) or classification (treating each star level as a distinct bucket). Usually, the goal of your analysis determines which one you choose.

Did You Know?

Most of the Exam SRM syllabus focuses on Supervised Learning. However, Principal Component Analysis (PCA) and Clustering (which you will see later) are the two big Unsupervised techniques you need to know!

4. Summary and Key Takeaways

To wrap up this section, let's look at a quick decision tree for your modeling mindset:

Step 1: Do I have a target output (\( Y \))?
• Yes: This is Supervised Learning. (Proceed to Step 2)
• No: This is Unsupervised Learning.

Step 2: Is my target (\( Y \)) a number or a category?
• Number: Use a Regression model.
• Category: Use a Classification model.

Key Points to Remember:

• Supervised models are used for prediction.
• Unsupervised models are used for discovery and understanding data structure.
• Quantitative = Numbers = Regression.
• Qualitative = Labels/Categories = Classification.

Great job! You've just laid the foundation for the entire SRM curriculum. In the next sections, we will start looking at the specific math and models used to actually perform these tasks!