Naive Bayes Classifier Explained : Applications and Practice Problems of Naive Bayes Classifier
Note: This article was originally published on Sep 13th, 2015 and updated on Sept 11th, 2017
Overview
 Understand one of the most popular and simple machine learning classification algorithms, the Naive Bayes algorithm
 It is based on the Bayes Theorem for calculating probabilities and conditional probabilities
 Learn how to implement the Naive Bayes Classifier or bayesian classification in R and Python
Introduction
Here’s a situation you’ve got into in your data science project:
You are working on a classification problem and have generated your set of hypothesis, created features and discussed the importance of variables. Within an hour, stakeholders want to see the first cut of the model.
What will you do? You have hundreds of thousands of data points and quite a few variables in your training data set. In such a situation, if I were in your place, I would have used ‘Naive Bayes‘, which can be extremely fast relative to other classification algorithms. It works on Bayes theorem of probability to predict the class of unknown data sets.
In this article, I’ll explain the basics of naive bayes in machine learning, so that next time when you come across large data sets, you can bring naive bayes classification algorithm in machine learning to action. In addition, if you are a newbie in Python or R, you should not be overwhelmed by the presence of available codes in this article.
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Table of Contents
 What is Naive Bayes algorithm?
 How Naive Bayes Algorithms works?
 What are the Pros and Cons of using Naive Bayes?
 4 Applications of Naive Bayes Algorithm
 Steps to build a basic Naive Bayes Model in Python
 Tips to improve the power of Naive Bayes Model
What is Naive Bayes algorithm?
It is a classification technique based on Bayes’ Theorem with an assumption of independence among predictors. In simple terms, a Naive Bayes classifier assumes that the presence of a particular feature in a class is unrelated to the presence of any other feature.
For example, a fruit may be considered to be an apple if it is red, round, and about 3 inches in diameter. Even if these features depend on each other or upon the existence of the other features, all of these properties independently contribute to the probability that this fruit is an apple and that is why it is known as ‘Naive’.
Naive Bayes model is easy to build and particularly useful for very large data sets. Along with simplicity, Naive Bayes is known to outperform even highly sophisticated classification methods.
Bayes theorem provides a way of calculating posterior probability P(cx) from P(c), P(x) and P(xc). Look at the equation below:
 P(cx) is the posterior probability of class (c, target) given predictor (x, attributes).
 P(c) is the prior probability of class.
 P(xc) is the likelihood which is the probability of predictor given class.
 P(x) is the prior probability of predictor.
How Naive Bayes algorithm works?
Let’s understand it using an example. Below I have a training data set of weather and corresponding target variable ‘Play’ (suggesting possibilities of playing). Now, we need to classify whether players will play or not based on weather condition. Let’s follow the below steps to perform it.
Step 1: Convert the data set into a frequency table
Step 2: Create Likelihood table by finding the probabilities like Overcast probability = 0.29 and probability of playing is 0.64.
Step 3: Now, use Naive Bayesian equation to calculate the posterior probability for each class. The class with the highest posterior probability is the outcome of prediction.
Problem: Players will play if weather is sunny. Is this statement is correct?
We can solve it using above discussed method of posterior probability.
P(Yes  Sunny) = P( Sunny  Yes) * P(Yes) / P (Sunny)
Here we have P (Sunny Yes) = 3/9 = 0.33, P(Sunny) = 5/14 = 0.36, P( Yes)= 9/14 = 0.64
Now, P (Yes  Sunny) = 0.33 * 0.64 / 0.36 = 0.60, which has higher probability.
Naive Bayes uses a similar method to predict the probability of different class based on various attributes. This algorithm is mostly used in text classification and with problems having multiple classes.
What are the Pros and Cons of Naive Bayes?
Pros:
 It is easy and fast to predict class of test data set. It also perform well in multi class prediction
 When assumption of independence holds, a Naive Bayes classifier performs better compare to other models like logistic regression and you need less training data.
 It perform well in case of categorical input variables compared to numerical variable(s). For numerical variable, normal distribution is assumed (bell curve, which is a strong assumption).
Cons:
 If categorical variable has a category (in test data set), which was not observed in training data set, then model will assign a 0 (zero) probability and will be unable to make a prediction. This is often known as “Zero Frequency”. To solve this, we can use the smoothing technique. One of the simplest smoothing techniques is called Laplace estimation.
 On the other side naive Bayes is also known as a bad estimator, so the probability outputs from predict_proba are not to be taken too seriously.
 Another limitation of Naive Bayes is the assumption of independent predictors. In real life, it is almost impossible that we get a set of predictors which are completely independent.
4 Applications of Naive Bayes Algorithms
 Real time Prediction: Naive Bayes is an eager learning classifier and it is sure fast. Thus, it could be used for making predictions in real time.
 Multi class Prediction: This algorithm is also well known for multi class prediction feature. Here we can predict the probability of multiple classes of target variable.
 Text classification/ Spam Filtering/ Sentiment Analysis: Naive Bayes classifiers mostly used in text classification (due to better result in multi class problems and independence rule) have higher success rate as compared to other algorithms. As a result, it is widely used in Spam filtering (identify spam email) and Sentiment Analysis (in social media analysis, to identify positive and negative customer sentiments)
 Recommendation System: Naive Bayes Classifier and Collaborative Filtering together builds a Recommendation System that uses machine learning and data mining techniques to filter unseen information and predict whether a user would like a given resource or not
How to build a basic model using Naive Bayes in Python and R?
Again, scikit learn (python library) will help here to build a Naive Bayes model in Python. There are three types of Naive Bayes model under the scikitlearn library:

Gaussian: It is used in classification and it assumes that features follow a normal distribution.

Multinomial: It is used for discrete counts. For example, let’s say, we have a text classification problem. Here we can consider Bernoulli trials which is one step further and instead of “word occurring in the document”, we have “count how often word occurs in the document”, you can think of it as “number of times outcome number x_i is observed over the n trials”.

Bernoulli: The binomial model is useful if your feature vectors are binary (i.e. zeros and ones). One application would be text classification with ‘bag of words’ model where the 1s & 0s are “word occurs in the document” and “word does not occur in the document” respectively.
Python Code:
Try out the below code in the coding window and check your results on the fly!
R Code:
require(e1071) #Holds the Naive Bayes Classifier Train < read.csv(file.choose()) Test < read.csv(file.choose()) #Make sure the target variable is of a twoclass classification problem only levels(Train$Item_Fat_Content) model < naiveBayes(Item_Fat_Content~., data = Train) class(model) pred < predict(model,Test) table(pred)
Above, we looked at the basic Naive Bayes model, you can improve the power of this basic model by tuning parameters and handle assumption intelligently. Let’s look at the methods to improve the performance of Naive Bayes Model. I’d recommend you to go through this document for more details on Text classification using Naive Bayes.
Tips to improve the power of Naive Bayes Model
Here are some tips for improving power of Naive Bayes Model:
 If continuous features do not have normal distribution, we should use transformation or different methods to convert it in normal distribution.
 If test data set has zero frequency issue, apply smoothing techniques “Laplace Correction” to predict the class of test data set.
 Remove correlated features, as the highly correlated features are voted twice in the model and it can lead to over inflating importance.
 Naive Bayes classifiers has limited options for parameter tuning like alpha=1 for smoothing, fit_prior=[TrueFalse] to learn class prior probabilities or not and some other options (look at detail here). I would recommend to focus on your preprocessing of data and the feature selection.
 You might think to apply some classifier combination technique like ensembling, bagging and boosting but these methods would not help. Actually, “ensembling, boosting, bagging” won’t help since their purpose is to reduce variance. Naive Bayes has no variance to minimize.
End Notes
In this article, we looked at one of the supervised machine learning algorithm “Naive Bayes” mainly used for classification. Congrats, if you’ve thoroughly & understood this article, you’ve already taken you first step to master this algorithm. From here, all you need is practice.
Further, I would suggest you to focus more on data preprocessing and feature selection prior to applying Naive Bayes algorithm.0 In future post, I will discuss about text and document classification using naive bayes in more detail.
Did you find this article helpful? Please share your opinions / thoughts in the comments section below.
You can use the following free resource to learn Naive Bayes
44 thoughts on "Naive Bayes Classifier Explained : Applications and Practice Problems of Naive Bayes Classifier"
Arun CR says: September 14, 2015 at 5:36 am
Hi Sunil , From the weather and play table which is table [1] we know that frequency of sunny is 5 and play when sunny is 3 no play when suny is 2 so probability(play/sunny) is 3/5 = 0.6 Why do we need conditional probabilty to solve this? Is there problems that can be solved only using conditional probability. can you suggest such examples. Thanks, ArunArun CR says: September 14, 2015 at 5:42 am
Great article and provides nice information.Nishi Singh says: December 12, 2015 at 10:35 am
Amazing content and useful informationmatt says: January 24, 2016 at 4:42 am
Arun, An example of a problem that requires the use of conditional probability is the Monty Hall problem. https://en.wikipedia.org/wiki/Monty_Hall_problem Conditional probability is used to solve this particular problem because the solution depends on Bayes' Theorem. Which was described earlier in the article.Leena says: February 08, 2016 at 5:59 am
I'm new to machine learning and Python.Could you please help to read data from CSV and to separate the same data set to training and test dataSushma honnidige says: March 07, 2016 at 2:44 pm
very useful article.RAJKUMAR says: March 16, 2016 at 1:30 pm
Very nice....but...if u dont mind...can you please give me that code in JAVA ...Erdem Karakoylu says: March 17, 2016 at 2:26 pm
It's a trivial example for illustration. The "Likelihood table" (a confusing misnomer, I think) is in fact a probability table that has the JOINT weather and play outcome probabilities in the center, and the MARGINAL probabilities of one variable (from integrating out the other variable from the joint) on the side and bottom. Say, weather type = w and play outcome = p. P(w,p) is the joint probabilities and P(p) and P(w) are the marginals. Bayes rule described above by Sunil stems from: P(w,p) = P(wp) * P(p) = P(pw) * P(w). From the center cells we have P(w,p) and from the side/bottom we get P(p) and P(w). Depending on what you need to calculate, it follows that: (1): P(wp) = P(w,p) / P(p) and (2:)P(pw) = P(w,p) / P(w), which is what you did with P(sunny,yes) = 3/14 and P(w) = 5/14, yielding (3/14 ) ( 14/5), with the 14's cancelling out. The main Bayes take away is that often, one of the two quantities above, P(wp) or P(pw) is much harder to get at than the other. So if you're a practitioner you'll come to see this as one of two mathematical miracles regarding this topic, the other being the applicability of Markov Chain Monte Carlo in circumventing some nasty integrals Bayes might throw at you. But I digress. Best, Erdem.jitesh says: April 05, 2016 at 3:20 am
is it possible to classify new tuple in orange data mining tool??SPGupta says: April 11, 2016 at 4:43 pm
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Thanks for tips to improve the performance of models, that 's really precious experience.Leanna Partridge says: May 11, 2016 at 8:18 am
Nice piece  Just to add my thoughts , people require a CA OCF1 , We used a sample document here http://goo.gl/ibPgs2Miguel Batista says: May 11, 2016 at 9:54 am
Hi, I have a question regarding this statement: 'If continuous features do not have normal distribution, we should use transformation or different methods to convert it in normal distribution.' Can you provide an example or a link to the techniques? Thank you, MBbd tv says: June 06, 2016 at 2:45 am
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Great article! Thanks. Are there any similar articles for other classification algorithms specially target towards textual features and mix of textual/numeric features?John Siano says: July 21, 2016 at 3:27 am
I had the same question. Have you found an answer? Thanks!Nick says: August 19, 2016 at 6:29 am
great article with basic clarity.....nice oneCatherine says: August 29, 2016 at 5:18 pm
This article is extremely clear and well laidout. Thank you!pangavhane nitin says: August 31, 2016 at 8:41 am
tyalfiya says: August 31, 2016 at 9:26 am
Explanation given in simple word. Well explained! Loved this article.Chris Rucker says: September 01, 2016 at 7:02 pm
The 'y' should be capitalized in your code  great article though.Akash Swamy says: September 06, 2016 at 7:24 am
This is the best explanation of NB so far simple and short :)John says: September 09, 2016 at 5:20 pm
Great article! Really enjoyed it. Just wanted to point out a small error in the Python code. Should be a capital "Y" in the predict like so : model.fit(x, Y) Thanks!Adnan says: September 20, 2016 at 5:12 am
Is this dataset related to weather? I am confused as a newbie. Can you please guide?Ismael Ezequiel says: October 15, 2016 at 12:12 am
import pandas as pd person = pd.read_csv('example.csv') mask = np.random.rand(len(sales)) < 0.8 train = sales[mask] test = sales[~mask]bh says: October 19, 2016 at 5:40 pm
best artical that help me to understand this conceptRichard says: October 25, 2016 at 7:52 pm
Am new to machine learning and this article was handy to me in understanding naive bayes especially the data on weather and play in the table. Thanks for sharing keep upLisa says: November 10, 2016 at 8:29 am
Thanks to you I can totally understand NB classifier.T B says: July 03, 2017 at 12:17 am
Really nice article, very usefull for concept building.AKshay says: July 04, 2017 at 8:40 pm
I didn't understand the 3rd step. Highest probability out of which probability values? >> Now, P (Yes  Sunny) = 0.33 * 0.64 / 0.36 = 0.60, which has higher probability. Higher than what?DN says: July 30, 2017 at 8:29 am
Concept explained well... nice ArticleRajeshwari says: August 31, 2017 at 2:36 pm
thanks nice artical that help me to understand this conceptamit Kumar yadav says: September 18, 2017 at 12:49 am
Good article and I am waiting for text and documents classification using naive base algorithm.Stella says: September 20, 2017 at 10:50 am
Superb information in just one blog.Enjoyed the simplicity.Thanks for the effort.Aishwarya says: November 26, 2017 at 10:12 pm
Good start point for beginnersAbdul Samad says: April 12, 2018 at 10:19 am
Weldone sanil I have a question regarding naive bayes,currently i am working on a project that is detect depression through naive bayes algorithm so plz suggest few links regarding my projects.i shall be gratefull to you. Thanku so muchAishwarya Singh says: April 16, 2018 at 4:37 pm
Hi Abdul, Refer this link.Tongesai Maune says: May 04, 2018 at 7:21 pm
I am not understanding the x and the y variables. Can someone help meAishwarya Singh says: May 06, 2018 at 1:24 pm
Hi Tongesai, X here represents the dependent variable and y is used for target variable (which is to be predicted).Artificial Neural Networks with EdgeBased Architecture – The Informaticists says: August 25, 2020 at 1:24 pm
[…] [4] Ray, Sunil. (2020, April 01). Learn Naive Bayes Algorithm: Naive Bayes Classifier Examples. Retrieved August 05, 2020, from https://www.analyticsvidhya.com/blog/2017/09/naivebayesexplained/ […]Jayer says: January 23, 2023 at 8:43 pm
Hello, how do i check which variables are significant using the naive Bayes algorithm in RSisay says: January 26, 2023 at 7:35 pm
It is nice, please make it open the code