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Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

How to Select Best Split in Decision Trees using Information Gain?

Himanshi Singh
Himanshi Singh Last Updated : 13 Dec, 2023
7 min read

Introduction

Decision trees are powerful tools for making predictions, but their effectiveness hinges on choosing the right splits. This article guides you through the concept of information gain, a key metric for selecting optimal splits and building robust decision trees. We’ll dive into calculations, explore examples, and equip you with the knowledge to navigate the decision tree landscape effectively.

Let’s begin!

Table of contents

Video Explanation

If you are more interested in learning concepts in an Audio-Visual format, We have this entire article explained in the video below. If not, you may continue reading.

Entropy and Purity

Consider these three nodes. Can you guess which of these nodes will require more information to describe them?

Information gain nodes

As you can see here, Node 3 is a pure node since it only contains one class. Whereas Node 2 is less pure and Node 1 is the most impure node out of all these three since it has a mixture of classes. And the percentage distribution in Node 1 is 50%. So as the impurity of the node increases, we require more information to describe them. And that’s why Node 1 will require more information as compared to the other nodes.

information nodes inequality

Information Gain Formula

So we can say that more impure nodes require more information to describe. Let’s continue an example. Look at the split, look at the right-hand side especially-

information gain split

It is leading to less homogeneous nodes compared to the split on the left, which is producing completely homogeneous nodes. What can you infer from that? Split on the right is giving less information gain. So we can say that a higher information gain leads to more homogeneous or pure nodes. The information gain can be calculated as:

information gain formula

Calculating Entropy

But wait, what is Entropy here? How can we calculate that? Let’s look at how we can do that.

We can calculate the entropy as:

entropy formula

Here P1, P2, and P3 are the percentages of each class in the node. Consider this node as an example-

class percentage

Here the percentage of students who play cricket is 0.5 and the percentage of students who do not play cricket is of course also 0.5

Now if I use the formula to calculate the entropy:

entropy application

The percentage of Play class is 0.5 multiplied by the log of 0.5 bases two minus the percentage of do not play, which is 0.5 multiply log of 0.5. Since the log of 0.5 bases two is -1, the entropy for this node will be 1. Let’s consider one more node-

You can see it’s a pure node as it only contains a single class. The percentage of students who play cricket, in this case, is 0 and who does not play is 1. So after applying the formula to these numbers, you can imagine that the entropy will come out to be zero. When you compare the entropy values here, we can see that:

Lower entropy means more pure node and higher entropy means less pure nodes.

Properties of Entropy

Let’s now look at the properties of Entropy.

  • Similar to Gini impurity and Chi-square, it also works only with the categorical target values.
  • Lesser the entropy higher the information gain, which will lead to more homogeneous or pure nodes.

These two are essentially, and basically the properties of entropy.

Steps to Calculate Entropy for a Split

  • We will first calculate the entropy of the parent node.
  • And then calculate the entropy of each child.
  • Finally, we will calculate the weighted average entropy of this split using the same steps that we saw while calculating the Gini.

Example: Performance vs. Class Split

The weight of the node will be the number of samples in that node divided by the total samples. In the parent note, if the weighted entropy of the child channel is greater than the parent node, we will not consider that split. As it’s returning more impure nodes compared to the parent node. Let’s use these two splits and calculate the entropy for both of the splits-

Steps to calculate Entropy for a Split

Let’s start with the student performance in class. This is the split we got based on the performance that you’re very familiar with this by now-

information gain entropy process

the first step is to calculate the entropy for the parent. Now, the probability of playing and not playing cricket is 0.5 each, as 50% of students are playing cricket. So the entropy for the parent node will be as shown here:

entropy parent

and it comes out to be 1. Similarly for the sub-node “Above average”, the probability of playing is 0.57, and the probability of not playing is 0.43. When you plug in those values:

entropy for sub-node

The entropy comes out to be 0.98. For the sub-node “Below average”, we do the same thing, the probability of playing is 0.33 and of not playing is 0.67. And when we plug those values into the formula, we get:

entropy for sub-node below average

Finally, the weighted entropy for the split on performance in class will be the sum of the weight of that node multiplied by the entropy of that node-

weighted entropy

The performance in class entropy will be around 0.959. Here we can see that this weighted entropy is lower than the entropy of the parent node. The parent node is 1 and the weighted entropy is 0.95. So we can say that it is returning more pure nodes compared to the parent node.

Similarly, we can calculate the entropy for “the split on Class” using the same steps that we just saw:

he split on Class
Information gain - split on class

Here we have calculated all the values. I’d advise you to calculate them on your own. Take a pen and paper, plug-in these values into the formula, and compare them with these results.

The weighted entropy for the split on “the Class” variable comes out with 0.722. Now we will compare the entropies of two splits, which are 0.959 for “Performance in class” and 0.722 for the split on “the Class” variable. Information Gain is calculated as:

information gain practical

Remember the formula we saw earlier, and these are the values we get when we use that formula-

split

For “the Performance in class” variable information gain is 0.041 and for “the Class” variable it’s 0.278. Lesser entropy or higher Information Gain leads to more homogeneity or the purity of the node. And hence split on the Class variable will produce more pure nodes.

And this is how we can make use of entropy and information gain to decide the best split.

Conclusion

In this article, we saw one more algorithm used for deciding the best split in the decision trees which is Information Gain. This algorithm is also used for the categorical target variables.

If you are looking to kick start your Data Science Journey and want every topic under one roof, your search stops here. Check out Analytics Vidhya’s Certified AI & ML BlackBelt Plus Program

Frequently Asked Questions

Q1. What is the purpose of the information gain measure in a decision tree algorithm?

A. Information gain evaluates the effectiveness of a feature in decision trees by assessing the reduction in uncertainty or entropy when that feature is utilized for splitting.

Q2. What are the drawbacks of using information gain in decision trees?

A. Information gain may exhibit bias toward attributes with more levels, struggle with continuous features, and be sensitive to irrelevant attributes, limiting its robustness.

Q3. How do Gini, entropy, and information gain differ in decision trees?

A. Gini measures impurity, entropy assesses disorder, and information gain quantifies the reduction in uncertainty when a node is split. These metrics play distinct roles in the decision tree algorithm.

Q4. Can information gain in a decision tree be negative?

A. No, information gain in a decision tree cannot be negative. It signifies the positive reduction in uncertainty achieved by splitting nodes based on a specific feature, guiding the constructive tree-building process.

If you have any queries let me know in the comment section!

Himanshi Singh
Himanshi Singh

I’m a data lover who enjoys finding hidden patterns and turning them into useful insights. As the Manager - Content and Growth at Analytics Vidhya, I help data enthusiasts learn, share, and grow together. 

Thanks for stopping by my profile - hope you found something you liked :)

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