I. Introduction
“In God we trust. All others must bring data.” – W. Edwards Deming
If there’s one thing I’ve learned in my years working with machine learning models, it’s this: your model is only as good as the decisions it makes. And when it comes to decision-making in machine learning, decision trees are one of the most intuitive and powerful tools out there.
Think about it—every decision we make in life follows a branching pattern. Should you go to work today? Yes or no? If yes, should you take the bus or drive? If no, should you rest or work from home? Every choice leads to another, forming a natural tree-like structure. Decision trees work the same way, except they use data to decide the best splits.
Why Decision Trees Matter
I’ve used decision trees in projects ranging from fraud detection to medical diagnosis, and the reason they’re so popular is simple: they’re easy to understand and extremely effective. Unlike black-box models like neural networks, decision trees provide clear reasoning for their choices.
But here’s the thing: a tree is only as good as the way it splits the data. Split poorly, and you get a weak, inaccurate model. Split well, and you create a decision-making powerhouse. This is where Information Gain comes in.
What is Information Gain?
I remember the first time I tried to optimize a decision tree and noticed it was making terrible splits. The problem? The model wasn’t choosing the most informative features. This is exactly why Information Gain exists—it’s a measure of how much a feature reduces uncertainty in the data. In simple terms, it tells us, “If we split the data here, how much more organized will it become?”
In this guide, I’ll take you through everything you need to know about Information Gain—how it works, why it’s better than some alternatives, and how to use it effectively. I’ll also share some lessons from my own experience and some pitfalls you should avoid.
Let’s dive in.
II. The Fundamentals of Decision Trees
How Decision Trees Work
At their core, decision trees follow a simple rule: they repeatedly split the data into smaller groups until they reach a stopping condition. But not all splits are equal—some create pure groups (where all the data belongs to one class), while others leave a mess.
In every decision tree I’ve built, I’ve had to carefully consider how splits happen. The basic components are:
- Nodes – Decision points where data is split
- Branches – The different paths the data can take
- Leaves – The final outcomes, where the classification is decided
Each time the tree makes a split, it’s essentially answering a yes/no question based on the data. The goal is to make these questions as useful as possible—which is where Information Gain comes in.
Splitting Criteria: Why Information Gain is So Important
There are multiple ways to decide the best split in a decision tree:
- Gini Index – Measures impurity by calculating how often a randomly chosen element would be misclassified.
- Information Gain (based on Entropy) – Measures how much uncertainty is reduced after a split.
- Chi-Square, Variance Reduction, etc. – Less common methods used in specialized cases.
I’ve personally found Information Gain to be one of the most reliable and intuitive approaches. Why? Because it directly measures how much knowledge we gain from a split. If a feature doesn’t help reduce uncertainty, why even use it?
Overfitting Risks: Why More Splits Aren’t Always Better
Early in my career, I made a classic mistake: I let my decision trees grow too deep. The result? A perfect model that completely failed on new data.
This is the biggest risk with decision trees—overfitting. If a tree keeps splitting based on minor details, it memorizes the training data instead of learning patterns. Information Gain can help here, but it’s not enough on its own. That’s why techniques like pruning and setting depth limits are crucial.
III. Understanding Entropy: The Foundation of Information Gain
“If you can’t explain it simply, you don’t understand it well enough.” – Albert Einstein
I remember when I first encountered entropy in machine learning. I had seen the formula before, but it didn’t immediately click. The definitions all talked about “measuring impurity” or “quantifying disorder,” but they didn’t explain what that actually meant in practice. It wasn’t until I broke it down into real-world decision-making that I truly understood how entropy drives Information Gain.
Definition of Entropy
Let’s get straight to it. In decision trees, entropy measures uncertainty in a dataset. The formula looks like this:
Where:
- H(S)H(S)H(S) is the entropy of dataset SSS.
- pip_ipi is the probability of class iii.
- ccc is the total number of classes.
The more mixed the classes in your dataset, the higher the entropy. The more pure (i.e., mostly one class), the lower the entropy.
Intuition Behind Entropy: Why It Matters
Here’s how I like to think about entropy:
Imagine you’re sorting emails into two folders: Spam and Not Spam.
- Case 1 – Pure Dataset (Low Entropy): If you open a folder and see only spam emails, there’s no uncertainty—you already know the classification. Entropy is low.
- Case 2 – Mixed Dataset (High Entropy): If the folder has a random mix of spam and non-spam emails, you have more uncertainty. Entropy is high.
A good decision tree split is one that reduces this uncertainty, pushing the dataset towards lower entropy.
Example Calculation: Understanding Entropy with Numbers
Let’s say you have a dataset of 10 emails:
- 6 are spam
- 4 are not spam
The entropy is calculated as:
Using logarithm values:
Since 0.970 is closer to 1, the dataset has high uncertainty—meaning we need a stronger split to improve classification.
Now, let’s move to Information Gain—this is where things get interesting.
IV. Information Gain Explained
“All models are wrong, but some are useful.” – George Box
If entropy tells us how messy the data is, Information Gain tells us how much cleaner it gets after a split. The higher the Information Gain, the better the feature is at making decisions.
Mathematical Definition of Information Gain
Here’s the formula:
Where:
- H(S) = Entropy before the split
- Sj = The subset created by the split
- ∣Sj∣ = The proportion of instances in each subset
- H(Sj) = Entropy of each subset
In simple terms: Information Gain measures how much uncertainty decreases when we split on a specific feature.
How Information Gain Measures Improvement
Let’s continue with our email spam example.
Say we introduce a new feature: “Does the email contain the word ‘free’?”
- If yes → 5 spam, 1 not spam (entropy = 0.65)
- If no → 1 spam, 3 not spam (entropy = 0.81)
The weighted entropy after the split is:
Now, let’s compute Information Gain:
A positive number! This tells us splitting on the word “free” reduces uncertainty, making it a valuable feature.
Intuitive Understanding: Real-Life Analogy
Think of Information Gain like cleaning a messy room.
- Before organizing (High Entropy) → Clothes, books, and gadgets scattered everywhere.
- After sorting into shelves and drawers (Low Entropy) → Everything is neatly arranged.
The more organized the room becomes after sorting, the more Information Gain we achieve. In decision trees, a good feature organizes the data into meaningful groups—just like a good cleaning system tidies up a room.
V. Practical Example of Information Gain Calculation
“In theory, there is no difference between theory and practice. In practice, there is.” – Yogi Berra
When I first started working with decision trees, I understood the concept of Information Gain, but I wasn’t truly comfortable with it until I calculated it manually. Seeing the numbers change before my eyes made everything click. So, let’s walk through a real dataset, the same way I did when I was learning.
Step-by-Step Example: Calculating Information Gain
Imagine we’re building a simple decision tree to classify whether a customer will buy a product based on one feature: “Does the customer have a discount coupon?”
| Customer | Has Coupon? | Purchased? |
|---|---|---|
| 1 | Yes | Yes |
| 2 | No | No |
| 3 | Yes | Yes |
| 4 | No | No |
| 5 | No | No |
| 6 | Yes | No |
| 7 | Yes | Yes |
| 8 | No | No |
| 9 | Yes | Yes |
| 10 | No | No |
Step 1: Calculate Initial Entropy
Before splitting the dataset, let’s calculate the entropy of the target variable (Purchased?).
- Total instances = 10
- Customers who purchased (Yes) = 4
- Customers who didn’t purchase (No) = 6
Using the entropy formula:
So, our dataset has an entropy of 0.971, meaning there’s still quite a bit of uncertainty in our target variable.
Step 2: Split the Data on “Has Coupon?” and Calculate New Entropy
Now, let’s split the dataset into two groups:
- Customers who have a coupon
- Customers who don’t have a coupon
- Subset 1 (Has Coupon = Yes) → 5 customers (4 purchased, 1 didn’t)
- Subset 2 (Has Coupon = No) → 5 customers (0 purchased, 5 didn’t)
Entropy for Subset 1 (Has Coupon = Yes):
Entropy for Subset 2 (Has Coupon = No):
Since all customers in this group did not purchase, entropy is 0 (pure class).
Step 3: Compute Information Gain
Boom! 💥 The Information Gain is 0.610, which tells us that splitting on “Has Coupon?” reduces uncertainty significantly. If I saw this in a real dataset, I’d immediately flag this feature as important for classification.
VI. Information Gain vs. Gini Index: When to Use Each
“All models are wrong, but some are useful.” – George Box
You might be wondering: “Why use Information Gain when we have the Gini Index?” That’s a question I asked myself when I first encountered decision trees. In practice, both metrics are used, but they have different strengths.
Core Differences: Entropy vs. Gini Index
At their core, both metrics measure impurity, but in different ways:
| Metric | Formula | What It Measures |
|---|---|---|
| Entropy (H) | −∑pilog2pi-\sum p_i \log_2 p_i−∑pilog2pi | Measures disorder in the dataset. |
| Gini Index | 1−∑pi21 – \sum p_i^21−∑pi2 | Measures probability of incorrect classification. |
Both range from 0 to 1, where 0 means pure and 1 means highly impure.
Pros and Cons: When to Use Each
| Metric | Pros | Cons |
|---|---|---|
| Information Gain (Entropy) | More mathematically rigorous, considers all class probabilities. | Computationally expensive (logarithms). |
| Gini Index | Faster, easier to compute. | Less sensitive to class probabilities, sometimes less accurate. |
When to Choose Each?
From my experience:
- If speed matters (large datasets), use Gini Index (it’s faster).
- If precision matters (imbalanced datasets), use Information Gain (it considers full class distribution).
- If using sklearn’s DecisionTreeClassifier, the default is Gini, but you can switch to entropy using
criterion="entropy".
In real projects, I often try both and compare results. Sometimes, Gini works just as well but runs much faster. Other times, Information Gain leads to a better decision boundary. Experimentation is key.
VII. Conclusion: Wrapping It All Up
If there’s one thing I’ve learned from working with decision trees, it’s this: understanding how your model makes decisions is just as important as getting high accuracy.
When I first started using decision trees, I relied on them blindly—plugging in data, tweaking hyperparameters, and hoping for the best. But the moment I dug deeper into Information Gain, everything changed. I could see why certain features were more important, why some splits were better than others, and—most importantly—how to improve my models.
Key Takeaways: What You Should Remember
Let’s quickly recap the essential points:
✅ Entropy measures impurity—lower entropy means a purer dataset.
✅ Information Gain tells you how much uncertainty is reduced by splitting on a feature.
✅ Higher Information Gain = A better split, making your decision tree more efficient.
✅ Gini Index is an alternative metric—faster but sometimes less informative.
✅ In practice, try both Information Gain and Gini Index to see what works best for your dataset.
What’s Next? Apply This Knowledge!
The best way to solidify your understanding is to get your hands dirty. Here’s what I recommend:
💡 Run an experiment: Take a dataset (like the Titanic dataset or a customer churn dataset) and manually compute Information Gain for a few features. See which ones contribute the most to decision-making.
💻 Try it in code: Use scikit-learn’s DecisionTreeClassifier with both "entropy" and "gini" as the criterion. Compare results—does one perform better? Is training time different?
📊 Visualize your tree: Use plot_tree() from scikit-learn or dtreeviz to see the splits in action.
Further Learning: Dive Deeper
If this topic fascinated you as much as it did me, here are some solid resources to keep going:
📖 Books:
- “Pattern Recognition and Machine Learning” by Christopher Bishop
- “Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow” by Aurélien Géron
📚 Official Documentation & Tutorials:
The more you explore, the more intuitive these concepts will become. I’d love to hear—how are you planning to apply Information Gain in your projects?
I’m a Data Scientist.