Anshul Saini — Published On September 15, 2021 and Last Modified On April 26th, 2023
Algorithm Beginner Machine Learning Technique


Boosting is an ensemble modeling technique that was first presented by Freund and Schapire in the year 1997. Since then, Boosting has been a prevalent technique for tackling binary classification problems. These algorithms improve the prediction power by converting a number of weak learners to strong learners.

The principle behind boosting algorithms is that we first build a model on the training dataset and then build a second model to rectify the errors present in the first model. This procedure is continued until and unless the errors are minimized and the dataset is predicted correctly. Boosting algorithms work in a similar way, it combines multiple models (weak learners) to reach the final output (strong learners).

AdaBoost Algorithm

In this article, we will understand the math behind different types of boosting algorithms.

There are mainly 3 types of boosting algorithms:

  • AdaBoost algorithm in Machine Learning
  • Gradient descent algorithm
  • Xtreme gradient descent algorithm

Here I will be focusing on the AdaBoost algorithm. Gradient Descent and XGboost will be covered in upcoming articles.

Learning Objectives

  • To understand what the AdaBoost algorithm is and how it works.
  • To understand what stumps are.
  • To find out how boosting algorithms help increase the accuracy of ML models.

This article was published as a part of the Data Science Blogathon

Table of Contents

What Is the AdaBoost Algorithm?

There are many machine learning algorithms to choose from for your problem statements. One of these algorithms for predictive modeling is called AdaBoost.

AdaBoost, also called Adaptive Boosting, is a technique in Machine Learning used as an Ensemble Method. The most common estimator used with AdaBoost is decision trees with one level which means Decision trees with only 1 split. These trees are also called Decision Stumps.

stump | AdaBoost Algorithm

What this algorithm does is that it builds a model and gives equal weights to all the data points. It then assigns higher weights to points that are wrongly classified. Now all the points with higher weights are given more importance in the next model. It will keep training models until and unless a lower error is received.

ensemble model | AdaBoost Algorithm

Let’s take an example to understand this, suppose you built a decision tree algorithm on the Titanic dataset, and from there, you get an accuracy of 80%. After this, you apply a different algorithm and check the accuracy, and it comes out to be 75% for KNN and 70% for Linear Regression.

We see the accuracy differs when we build a different model on the same dataset. But what if we use combinations of all these algorithms to make the final prediction? We’ll get more accurate results by taking the average of the results from these models. We can increase the prediction power in this way.

If you want to understand this visually, I strongly recommend you go through this article.

Here we will be more focused on mathematics intuition.

There is another ensemble learning algorithm called the gradient boosting algorithm. In this algorithm, we try to reduce the error instead of wights, as in AdaBoost. But in this article, we will only be focussing on the mathematical intuition of AdaBoost.

Understanding the Working of the AdaBoost Algorithm

Let’s understand what and how this algorithm works under the hood with the following tutorial.

Step 1 – The Image shown below is the actual representation of our dataset. Since the target column is binary, it is a classification problem. First of all, these data points will be assigned some weights. Initially, all the weights will be equal.

data | AdaBoost Algorithm

The formula to calculate the sample weights is:


Where N is the total number of data points

Here since we have 5 data points, the sample weights assigned will be 1/5.

Step 2 – We start by seeing how well “Gender” classifies the samples and will see how the variables (Age, Income) classify the samples.

We’ll create a decision stump for each of the features and then calculate the Gini Index of each tree. The tree with the lowest Gini Index will be our first stump.

Here in our dataset, let’s say Gender has the lowest gini index, so it will be our first stump.

Step 3 – We’ll now calculate the “Amount of Say” or “Importance” or “Influence” for this classifier in classifying the data points using this formula:

error | AdaBoost Algorithm


The total error is nothing but the summation of all the sample weights of misclassified data points.

Here in our dataset, let’s assume there is 1 wrong output, so our total error will be 1/5, and the alpha (performance of the stump) will be:

performance of stumps

Note: Total error will always be between 0 and 1.

0 Indicates perfect stump, and 1 indicates horrible stump.

error rate

From the graph above, we can see that when there is no misclassification, then we have no error (Total Error = 0), so the “amount of say (alpha)” will be a large number.

When the classifier predicts half right and half wrong, then the Total Error = 0.5, and the importance (amount of say) of the classifier will be 0.

If all the samples have been incorrectly classified, then the error will be very high (approx. to 1), and hence our alpha value will be a negative integer.

Step 4 – You must be wondering why it is necessary to calculate the TE and performance of a stump. Well, the answer is very simple, we need to update the weights because if the same weights are applied to the next model, then the output received will be the same as what was received in the first model.

The wrong predictions will be given more weight, whereas the correct predictions weights will be decreased. Now when we build our next model after updating the weights, more preference will be given to the points with higher weights.

After finding the importance of the classifier and total error, we need to finally update the weights, and for this, we use the following formula:

net weight sample

The amount of, say (alpha) will be negative when the sample is correctly classified.

The amount of, say (alpha) will be positive when the sample is miss-classified.

There are four correctly classified samples and 1 wrong. Here, the sample weight of that datapoint is 1/5, and the amount of say/performance of the stump of Gender is 0.69.

New weights for correctly classified samples are:

correctly classified | AdaBoost Algorithm

For wrongly classified samples, the updated weights will be:

wrongly classified

Note: See the sign of alpha when I am putting the values, the alpha is negative when the data point is correctly classified, and this decreases the sample weight from 0.2 to 0.1004. It is positive when there is misclassification, and this will increase the sample weight from 0.2 to 0.3988

new sample

We know that the total sum of the sample weights must be equal to 1, but here if we sum up all the new sample weights, we will get 0.8004. To bring this sum equal to 1, we will normalize these weights by dividing all the weights by the total sum of updated weights, which is 0.8004. So, after normalizing the sample weights, we get this dataset, and now the sum is equal to 1.

Step 5 – Now, we need to make a new dataset to see if the errors decreased or not. For this, we will remove the “sample weights” and “new sample weights” columns and then, based on the “new sample weights,” divide our data points into buckets.


Step 6 – We are almost done. Now, what the algorithm does is selects random numbers from 0-1. Since incorrectly classified records have higher sample weights, the probability of selecting those records is very high.

Suppose the 5 random numbers our algorithm take is 0.38,0.26,0.98,0.40,0.55.

Now we will see where these random numbers fall in the bucket, and according to it, we’ll make our new dataset shown below.

output | AdaBoost Algorithm

This comes out to be our new dataset, and we see the data point, which was wrongly classified, has been selected 3 times because it has a higher weight.

Step 9 – Now this act as our new dataset, and we need to repeat all the above steps i.e.

  1.  Assign equal weights to all the data points.
  2. Find the stump that does the best job classifying the new collection of samples by finding their Gini Index and selecting the one with the lowest Gini index.
  3. Calculate the “Amount of Say” and “Total error” to update the previous sample weights.
  4.  Normalize the new sample weights.

Iterate through these steps until and unless a low training error is achieved.

Suppose, with respect to our dataset, we have constructed 3 decision trees (DT1, DT2, DT3) in a sequential manner. If we send our test data now, it will pass through all the decision trees, and finally, we will see which class has the majority, and based on that, we will do predictions
for our test dataset.


You have finally mastered this algorithm if you understand each and every line of this article.

We started by introducing you to what Boosting is and what are its various types to make sure that you understand the Adaboost classifier and where AdaBoost falls exactly. We then applied straightforward math and saw how every part of the formula worked.

In the next article, I will explain Gradient Descent and Xtreme Gradient Descent algorithm, which are a few more important Boosting techniques to enhance the prediction power.

If you want to know about the python implementation for beginners of the AdaBoost machine learning model from scratch, then visit this complete guide from analytics vidhya. This article mentions the difference between bagging and boosting, as well as the advantages and disadvantages of the AdaBoost algorithm.

Key Takeaways

  • In this article, we understood how boosting works.
  • We understood the maths behind adaboost.
  • We learned how weak learners are used as estimators to increase accuracy.

Frequently Asked Questions

Q1. Is the AdaBoost algorithm supervised or unsupervised?

A. Adaboost falls under the supervised learning branch of machine learning. This means that the training data must have a target variable. Using the adaboost learning technique, we can solve both classification and regression problems.

Q2. What are the advantages of the AdaBoost algorithm?

A. Lesser preprocessing is required, as you do not need to scale the independent variables. Each iteration in the AdaBoost algorithm uses decision stumps as individual models, so the preprocessing required is the same as decision trees. AdaBoost is less prone to overfitting as well. In addition to boosting weak learners, we can also fine-tune hyperparameters(learning_rate, for example) in these ensemble techniques to get even better accuracy.

Q3. How do you use the AdaBoost algorithm?

A. Much like random forests, decision trees, logistic regression, and svm classifiers, AdaBoost also requires the training data to have a target variable. This target variable could be either categorical or continuous. The scikit-learn library contains the Adaboost classifiers and regressors; hence we can use sklearn in python to create an adaboost model.

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About the Author

Anshul Saini

I am an undergraduate student currently in my last year majoring in Statistics (Bachelors of Statistics) and have a strong interest in the field of data science, machine learning, and artificial intelligence. I enjoy diving into data to discover trends and other valuable insights about the data. I am constantly learning and motivated to try new things.

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5 thoughts on "Master the AdaBoost Algorithm: Guide to Implementing & Understanding AdaBoost"

yash says: September 11, 2022 at 12:36 pm
why we randomly select number in step 6 and not directly the incorrect classified? Reply
Prosenjit Banerjee
Prosenjit Banerjee says: September 15, 2022 at 8:45 pm
What will happen if the total error is 0? How do we calculate performance of stump? Reply
Sourav says: October 03, 2022 at 11:39 am
Nice article. Thank you Reply
HASHIR BIN ABDUL AZEEZ says: October 14, 2022 at 9:55 am
we're selecting new dataset by bootstrapping technique. Reply
rtz says: December 30, 2022 at 8:59 am
Is this section in this correct in this article: “ The amount of say (alpha) will be negative when the sample is correctly classified. The amount of say (alpha) will be positive when the sample is miss-classified.” Should not be it reversed ? Reply

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