Multinomial Naive Bayes Explained: Function, Advantages & Disadvantages, Applications in 2021


There are thousands of softwares or tools for the analysis of numerical data but there are very few for texts. Multinomial Naive Bayes is one of the most popular supervised learning classifications that is used for the analysis of the categorical text data.

Text data classification is gaining popularity because there is an enormous amount of information available in email, documents, websites, etc. that needs to be analyzed. Knowing the context around a certain type of text helps in finding the perception of a software or product to users who are going to use it.

This article will give you a deep understanding of the multinomial Naive Bayes algorithm and all the concepts that are related to it. We go through a brief overview of the algorithm, how it works, its benefits, and its applications.

What is the Multinomial Naive Bayes algorithm?

Multinomial Naive Bayes algorithm is a probabilistic learning method that is mostly used in Natural Language Processing (NLP). The algorithm is based on the Bayes theorem and predicts the tag of a text such as a piece of email or newspaper article. It calculates the probability of each tag for a given sample and then gives the tag with the highest probability as output.

Naive Bayes classifier is a collection of many algorithms where all the algorithms share one common principle, and that is each feature being classified is not related to any other feature. The presence or absence of a feature does not affect the presence or absence of the other feature.

How Multinomial Naive Bayes works?

Naive Bayes is a powerful algorithm that is used for text data analysis and with problems with multiple classes. To understand Naive Bayes theorem’s working, it is important to understand the Bayes theorem concept first as it is based on the latter.

Bayes theorem, formulated by Thomas Bayes, calculates the probability of an event occurring based on the prior knowledge of conditions related to an event. It is based on the following formula:

P(A|B) = P(A) * P(B|A)/P(B)

Where we are calculating the probability of class A when predictor B is already provided.

P(B) = prior probability of B

P(A) = prior probability of class A

P(B|A) = occurrence of predictor B given class A probability

This formula helps in calculating the probability of the tags in the text.

Let us understand the Naive Bayes algorithm with an example. In the below given table, we have taken a data set of weather conditions that is sunny, overcast, and rainy. Now, we need to predict the probability of whether the players will play based on weather conditions. 

Must Read: Introduction to Naive Bayes

Training Data Set

Weather Sunny Overcast Rainy Sunny Sunny Overcast Rainy Rainy Sunny Rainy Sunny Overcast Overcast Rainy
Play No Yes Yes Yes Yes Yes No No Yes Yes No Yes Yes No


This can be easily calculated by following the below given steps:

Create a frequency table of the training data set given in the above problem statement. List the count of all the weather conditions against the respective weather condition.


Weather Yes No
Sunny 3 2
Overcast 4 0
Rainy 2 3
Total 9 5

Find the probabilities of each weather condition and create a likelihood table.

Weather Yes No
Sunny 3 2 =5/14(0.36)
Overcast 4 0 =4/14(0.29)
Rainy 2 3 =5/14(0.36)
Total 9 5
=9/14 (0.64) =5/14 (0.36)

Calculate the posterior probability for each weather condition using the Naive Bayes theorem. The weather condition with the highest probability will be the outcome of whether the players are going to play or not. 

Use the following equation to calculate the posterior probability of all the weather conditions: 

P(A|B) = P(A) * P(B|A)/P(B) 

After replacing variables in the above formula, we get:

P(Yes|Sunny) = P(Yes) * P(Sunny|Yes) / P(Sunny)

Take the values from the above likelihood table and put it in the above formula.

P(Sunny|Yes) = 3/9 = 0.33, P(Yes) = 0.64 and P(Sunny) = 0.36

Hence, P(Yes|Sunny) = (0.64*0.33)/0.36 = 0.60

P(No|Sunny) = P(No) * P(Sunny|No) / P(Sunny)

Take the values from the above likelihood table and put it in the above formula.

P(Sunny|No) = 2/5 = 0.40, P(No) = 0.36 and P(Sunny) = 0.36

P(No|Sunny) = (0.36*0.40)/0.36 = 0.6 = 0.40

The probability of playing in sunny weather conditions is higher. Hence, the player will play if the weather is sunny. 

Similarly, we can calculate the posterior probability of rainy and overcast conditions, and based on the highest probability; we can predict whether the player will play.

Checkout: Machine Learning Models Explained


The Naive Bayes algorithm has the following advantages:

  • It is easy to implement as you only have to calculate probability.
  • You can use this algorithm on both continuous and discrete data.
  • It is simple and can be used for predicting real-time applications.
  • It is highly scalable and can easily handle large datasets.


The Naive Bayes algorithm has the following disadvantages:

  • The prediction accuracy of this algorithm is lower than the other probability algorithms.
  • It is not suitable for regression. Naive Bayes algorithm is only used for textual data classification and cannot be used to predict numeric values.


Naive Bayes algorithm is used in the following places:

  • Face recognition
  • Weather prediction
  • Medical diagnosis
  • Spam detection
  • Age/gender identification
  • Language identification
  • Sentimental analysis
  • Authorship identification
  • News classification


It is worth learning the Multinomial Naive Bayes algorithm as it has so many applications in several industries, and the predictions made by this algorithm are real-quick. News classification is one of the most popular use cases of the Naive Bayes algorithm. It is highly used to classify news into different sections such as political, regional, global, and so on.

This article covers everything that you should know to get started with the Multinomial Naive Bayes algorithm and the working of Naïve Bayes classifier step-by-step. 

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