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# A Step by Step Guide to Implement Naive Bayes Algorithm in R

##### November 18, 2021

Naive Bayes is a machine learning algorithm based on the Bayes Theorem, and it’s used to solve classification problems. The Naive Bayes classifier is very effective and can be used with highly complex problems despite its simplicity. Due to its ability to handle highly complex tasks, the Naive Bayes has gained popularity in machine learning for a long time. Some Naive Bayes applications include; sentiment analysis, spam filtering, text classification, and much more.

This tutorial will discuss the Naive Bayes algorithm and its principles to deliver a solid and clear understanding of this tool. Later, we will discuss the real-world application of the Naive Bayes algorithm. Finally, we will implement and evaluate its performance using a confusion matrix in R.

### Prerequisites

To follow along with this tutorial, you’re required to have:

• R installed on your computer.
• Programming skills in R.
• A dataset that we will use in our implementation.
• Required packages installed, i.e.,
• install.packages(‘caTools’)
• install.packages(‘e1071’)

### Introduction to the Naive Bayes Algorithm

Before diving into Naive Bayes, we must first understand the Bayes Theorem and its assumptions. To understand this, we first consider a conditional probability from which the mathematical representation of the Bayes theorem is derived.

From the probability and statistic world, the conditional probability is defined as:

$p(A|B)=\frac{p(A\cap B)}{p(B)}$

Where:

• A and B are two events.
• $p(A|B)$ is the conditional probability. We read this as the probability of A given B.
• $p(A\cap B)=p(A, B)$ is called the joint probability, i.e., probability of A and B happening together.
• $p(B)$ is the probability of event ${B}$ .

From the probability rules: Sum: $p(A)=\sum_{all B} {p(A,B)}$ and,

Product: ${p(A,B)}=p(B|A)p(A)$

From the symmetry property $p(A, B) = p(B, A)$, thus, we can define:

$p(B|A)=\frac{p(A,B)}{p(A)}\rightarrow {p(A,B)}=p(B|A)p(A)$

This relationship defines how the product rule above comes about.

Using the rule above, we can rewrite our conditional probability as follows:

$p(A|B)=\frac{p(B|A)p(A)}{p(B)}$ which is the Bayes theorem.

Note that, introducing the sum rule on the $p{(B)}$, this theorem can be written as:

$p(A|B)=\frac{p(B|A)p(A))}{\sum_{all A} {p(B|A)p(A)}}$.

Now that we know the mathematical representation of the Bayes theorem let’s understand its components.

• The component $p(A|B)$ is called posterior. This quantity is defined as the probability of the hypothesis given data.
• The ${p(B|A)}$ is called likelihood. It’s is the probability of the data given the hypothesis.
• The $p(A)$ is called prior. It represents our belief about the distribution.
• The $p(B)$ is defined as the normalizing constant.

This term can as well be written as:

$p(B)=\sum_{all A} {p(B|A)p(A)}$

• $p(B)$ ensures that the sum of the posterior over all A values equals one.

The Bayes theorem assumes that events A and B are independent of each other. However, with real-world datasets, this assumption is not always valid. It’s usual for dataset features to be correlated.

Therefore, this assumption of the Bayes theorem based on this assumption remains to be ‘naive’. This is why in machine learning, this algorithm is called Naive Bayes Algorithm.

### Implementing Naive Bayes Algorithm

We will implement our model on a business dataset that contains information about customers who previously transacted with the business. The dataset consists of 400 customers, and each customer has information on their age, their estimated salary, and whether they bought a particular product or not.

Our task is to train a Naive Bayes classifier to understand the correlation between the features, i.e., Age, EstimatedSalary, and the Purchased target variable. The essence of this is to enable the business to predict which customer is likely to purchase their new product and accurately target them with valid ads from their social networks. The link to download this data is provided in the prerequisites section.

### Step 1: Data preprocessing

In this step, we will not dive into details of the data preprocessing steps. Instead, you can refer to this article for information on performing data preprocessing in r.

First, we need to install the required libraries. Let’s copy-paste and execute the code below on the console.

install.packages('caTools') # contains tools for data splitting
install.packages('e1071') # cointains the naive Bayes classifier model


However, we only need to install these packages if they’re not already in our system.

Next, we import our dataset and view the first five rows with the help of the head() function. To achieve this, let’s again run the code.

# Importing the dataset
# Looking at the first 10 observations of our dataset


Output:

As we can see, the data has two features, i.e., Age and EstimatedSalary with Purchased as the target variable. The target variable takes the value 1 for a customer who bought and 0 for a customer who didn’t buy the product.

The number on the rows corresponds to a particular customer. Hoping we now understand our data better, let’s continue with our preprocessing activity. The code snippet below concludes this activity.

# Encoding the target variable
data$Purchased = factor(data$Purchased, levels = c(0, 1))
# Splitting the data into training and test sets
library(caTools)
set.seed(123)
split = sample.split(data$Purchased, SplitRatio = 0.80) Train_set = subset(data, split == TRUE) Test_set = subset(dataset, split == FALSE) # Feature Scaling Train_set[-3] = scale(Train_set[-3]) Test_set[-3] = scale(Test_set[-3])  ### Step 2: Fitting the Naive Bayes classifier to the training set To get started, let’s make sure that the e1071 package is installed on R. As we earlier said, we only install this package if it is not already installed on our systems. Otherwise, we proceed and load its library. library(e1071) # load the library classifier = naiveBayes(x = Train_set[-3], y = Train_set$Purchased) # Fits Naive Bayes Model to the training set


### Step 3: Predicting the test set results

# Predicting the test set output
y_predict = predict(classifier, newdata = Test_set[-3])

# Creating a Confusion Matrix
conf_matrx = table(Test_set[, 3], y_predict)
conf_matrx


This is the result obtained from the confusion matrix:

From the confusion matrix shown above, we notice that out of 100%, the model could predict 86% of the data correctly with only 14% incorrect predictions. From this, it’s clear that our model has an accuracy of 86%. The accuracy of 86% is a good score, and thus we can conclude that our classifier is able to classify our data accurately.

### Conclusion

In this tutorial, we have learned the Naive Bayes classifier’s theory. First, we showed how to derive a mathematical formula of this classifier from the basic conditional probability. Later, we showed how to implement the Naive Bayes classifier in R and evaluated its performance using a confusion matrix.

From the confusion matrix, we saw its ability to classify the data by giving a relatively incredible score. We can challenge ourselves by implementing tasks to handle problems such as email classification, transaction classification, and health data to classify tumors and other diseases.

Happy coding!

Peer Review Contributions by: Willies Ogola