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6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
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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
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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
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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
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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
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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
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Naive Bayes Algorithm: A Complete guide for Data Science Enthusiasts

Anshul
Anshul Last Updated : 03 May, 2024
8 min read
Naive Bayes Algorithm

Introduction

In this article, we will discuss the mathematical intuition behind Naive Bayes Classifiers, and we’ll also see how to implement this on Python.Also We Will Discuss about Naive Bayes algorithm in Machine Learning

This model is easy to build and is mostly used for large datasets. It is a probabilistic machine learning model that is used for classification problems. The core of the classifier depends on the Naive Bayes theorem with an assumption of independence among predictors. That means changing the value of a feature doesn’t change the value of another feature.

Why is it called Naive?

It is called Naive because of the assumption that 2 variables are independent when they may not be. In a real-world scenario, there is hardly any situation where the features are independent.

Naive Bayes does seem to be a simple yet powerful algorithm. But why is it so popular?

Since it is a probabilistic approach, the predictions can be made real quick. It can be used for both binary and multi-class classification problems.

Before we dive deeper into this topic we need to understand what is “Conditional probability”, what is “Bayes’ theorem” and how conditional probability help’s us in Bayes’ theorem.

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

Table of contents

What is Naive Bayes Algorithm?

The Naive Bayes algorithm is a popular and simple classification algorithm used in machine learning. It works by calculating the probability of an item belonging to a certain class based on its features.

Naive Bayes Algorithm in Machine Learning

Naive Bayes is a simple but powerful method in machine learning used for guessing categories of things. Imagine sorting emails into spam or inbox. Naive Bayes looks at each word (like a clue) and predicts how likely it is to be spam based on past emails. It assumes these words aren’t connected (not always true!), but it’s fast and works well, making it a popular choice for many tasks.sharemore_vert

Conditional Probability for Naive Bayes

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

Let’s start understanding this definition with examples.

Suppose I ask you to pick a card from the deck and find the probability of getting a king given the card is clubs.

Observe carefully that here I have mentioned a condition that the card is clubs.

Now while calculating the probability my denominator will not be 52, instead, it will be 13 because the total number of cards in clubs is 13.

Since we have only one king in clubs the probability of getting a KING given the card is clubs will be 1/13 = 0.077.

Let’s take one more example,

Consider a random experiment of tossing 2 coins. The sample space here will be:

S = {HH, HT, TH, TT}

If a person is asked to find the probability of getting a tail his answer would be 3/4 = 0.75

Now suppose this same experiment is performed by another person but now we give him the condition that both the coins should have heads. This means if event A: ‘Both the coins should have heads’, has happened then the elementary outcomes {HT, TH, TT} could not have happened. Hence in this situation, the probability of getting heads on both the coins will be 1/4 = 0.25

From the above examples, we observe that the probability may change if some additional information is given to us. This is exactly the case while building any machine learning model, we need to find the output given some features.

Mathematically, the conditional probability of event A given event B has already happened is given by:

conditional probability | Naive Bayes Algorithm

Image Source: Author

Bayes’ Rule

Now we are prepared to state one of the most useful results in conditional probability: Bayes’ Rule.

Bayes’ theorem which was given by Thomas Bayes, a British Mathematician, in 1763 provides a means for calculating the probability of an event given some information.

Mathematically Bayes’ theorem can be stated as:

bayes rule

 

Basically, we are trying to find the probability of event A, given event B is true.

Here P(B) is called prior probability which means it is the probability of an event before the evidence

P(B|A) is called the posterior probability i.e., Probability of an event after the evidence is seen.

With regards to our dataset, this formula can be re-written as:

formula | Naive Bayes Algorithm

Y: class of the variable

X: dependent feature vector (of size n)

Bayes rule use

Image Source: Author

What is Naive Bayes?

Bayes’ rule provides us with the formula for the probability of Y given some feature X. In real-world problems, we hardly find any case where there is only one feature.

When the features are independent, we can extend Bayes’ rule to what is called Naive Bayes which assumes that the features are independent that means changing the value of one feature doesn’t influence the values of other variables and this is why we call this algorithm “NAIVE”

Naive Bayes can be used for various things like face recognition, weather prediction, Medical Diagnosis, News classification, Sentiment Analysis, and a lot more.

When there are multiple X variables, we simplify it by assuming that X’s are independent, so

bayes rule for multiple X | Naive Bayes Algorithm

 

For n number of X, the formula becomes Naive Bayes:

The n number of X

Which can be expressed as:

representation | Naive Bayes Algorithm

Since the denominator is constant here so we can remove it. It’s purely your choice if you want to remove it or not. Removing the denominator will help you save time and calculations.

equation

This formula can also be understood as:

Final formula | Naive Bayes Algorithm
Image Source: Author

There are a whole lot of formulas mentioned here but worry not we will try to understand all this with the help of an example.

Naive Bayes Example

Let’s take a dataset to predict whether we can pet an animal or not.

example dataset

 

Image Source: Author

Assumptions of Naive Bayes

· All the variables are independent. That is if the animal is Dog that doesn’t mean that Size will be Medium

· All the predictors have an equal effect on the outcome. That is, the animal being dog does not have more importance in deciding If we can pet him or not. All the features have equal importance.

We should try to apply the Naive Bayes Classifier formula on the above dataset however before that, we need to do some precomputations on our dataset.

We need to find P(xi|yj) for each xi in X and each yj in Y. All these calculations have been demonstrated below:

assumptions | Naive Bayes Algorithm

Image Source: Author

 

We also need the probabilities (P(y)), which are calculated in the table below. For example, P(Pet Animal = NO) = 6/14.

probabilities | Naive Bayes Algorithm

 

Image Source: Author

Now if we send our test data, suppose test = (Cow, Medium, Black)

Probability of petting an animal :

Probability of petting an animal
Probability of petting an animal value

And the probability of not petting an animal:

probability of not petting an animal | Naive bayes algorithm
value

We know P(Yes|Test)+P(No|test) = 1

So, we will normalize the result:

normalize the result | probability of not petting an animal

We see here that P(Yes|Test) > P(No|Test), so the prediction that we can pet this animal is “Yes”.

Gaussian Naive Bayes

So far, we have discussed how to predict probabilities if the predictors take up discrete values. But what if they are continuous? For this, we need to make some more assumptions regarding the distribution of each feature. The different naive Bayes classifiers differ mainly by the assumptions they make regarding the distribution of P(xi | y). Here we’ll discuss Gaussian Naïve Bayes.

Gaussian Naïve Bayes is used when we assume all the continuous variables associated with each feature to be distributed according to Gaussian Distribution. Gaussian Distribution is also called Normal distribution.

The conditional probability changes here since we have different values now. Also, the (PDF)  probability density function of a normal distribution is given by:

Gaussian naive bayes

We can use this formula to compute the probability of likelihoods if our data is continuous.

Endnotes

Naive Bayes algorithms are mostly used in face recognition, weather prediction, Medical Diagnosis, News classification, Sentiment Analysis, etc. In this article, we learned the mathematical intuition behind Naive bayes algorithm in Machine learning.  You have already taken your first step to master this algorithm and from here all you need is practi

Frequently Asked Questions

Q1. Why is Naive Bayes algorithm used?

A. The Naive Bayes algorithm is used due to its simplicity, efficiency, and effectiveness in certain types of classification tasks. It’s particularly suitable for text classification, spam filtering, and sentiment analysis. It assumes independence between features, making it computationally efficient with minimal data. Despite its “naive” assumption, it often performs well in practice, making it a popular choice for various applications.

Q2. What is the Naive Bayes algorithm?

A. The Naive Bayes algorithm is a probabilistic classification technique based on Bayes’ theorem. It assumes that all features in the data are independent of each other, given the class label. It calculates the probability of a particular class for a given set of features and selects the class with the highest probability as the predicted class. It’s commonly used in text classification and spam filtering tasks.

Q3. What is Naive Bayes Classifier?

Naive Bayes is a simple yet powerful machine learning algorithm for classification. It uses Bayes theorem to predict the class of something (like spam or not spam) based on its features (like words in an email). It’s popular for its speed and accuracy, especially in text classification tasks.
pen_spark






Q4. What is naive Bayes classification algorithm in R?

Naive Bayes is a classification algorithm in R used for tasks like spam filtering. It predicts probabilities of an instance belonging to a class based on Bayes’ theorem.
Here’s the gist of implementing it:
Load libraries (mlbench, caret, e1071).
Prepare data (load, explore, pre-process).
Split data into training and testing sets.
Build the model using naiveBayes() function.
Make predictions using predict() on the model and testing data.
Evaluate the model’s performance (accuracy, precision, etc.).pen_spark


















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Anshul
Anshul

I have recently graduated with a Bachelor's degree in Statistics and am passionate about pursuing a career in the field of data science, machine learning, and artificial intelligence. Throughout my academic journey, I thoroughly enjoyed exploring data to uncover valuable insights and trends.

I am eager to continue learning and expanding my knowledge in the field of data science. I am particularly interested in exploring deep learning and natural language processing, and I am constantly seeking out new challenges to improve my skills. My ultimate goal is to use my expertise to help businesses and organizations make data-driven decisions and drive growth and success.

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Jayesh
Jayesh

I am Phd Student. My phd theses title is "prediction of student performance in higher education using machine learning" Can you please help how to build model using different ML algorithm to predict the performance of student

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Jayasurya
Jayasurya

if suppose my test is animal cat size medium color grey but here no probability value of cat and grey now how can I get correct classification?

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Ignus
Ignus

What is the p(Test)?

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