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What is Naive Bayes in Machine Learning

Naive Bayes is a simple but surprisingly powerful probabilistic machine learning algorithm used for predictive modeling and classification tasks. Some typical applications of Naive Bayes are spam filtering, sentiment prediction, classification of documents, etc. It is a popular algorithm mainly because it can be easily written in code and predictions can be made real quick which in turn increases the scalability of the solution. The Naive Bayes algorithm is traditionally considered the algorithm of choice for practical-based applications mostly in cases where instantaneous responses are required for user’s requests.It is based on the works of the Rev. Thomas Bayes and hence the name. Before starting off with Naive Bayes, it is important to learn about Bayesian learning, what is ‘Conditional Probability’ and ‘Bayes Rule’.Bayesian learning is a supervised learning technique where the goal is to build a model of the distribution of class labels that have a concrete definition of the target attribute. Naïve Bayes is based on applying Bayes' theorem with the naïve assumption of independence between each and every pair of features.What is Conditional Probability?Let us start with the primitives by understanding Conditional Probability with some examples.Example 1Consider you have a coin and fair dice. When you flip a coin, there is an equal chance of getting either a head or a tail. So you can say that the probability of getting heads or the probability of getting tails is 50%.Now if you roll the fair dice, the probability of getting 1 out of the 6 numbers would be 1/6 = 0.166. The probability will also be the same for other numbers on the dice.Example 2Consider another example of playing cards. You are asked to pick a card from the deck. Can you guess the probability of getting a king given the card is a heart?The given condition here is that the card is a heart, so the denominator has to be 13 (there are 13 hearts in a deck of cards) and not 52. Since there is only one king in hearts, so the probability that the card is a king given it is a heart is 1/13 = 0.077.So when you say the conditional probability of A given B, it refers to the probability of the occurrence of A given that B has already occurred. This is a typical example of conditional probability.Mathematically, the conditional probability of A given B can be defined as P(A AND B) / P(B).Example 3Let us see another slightly complicated example to understand conditional probability better.Consider a school with a total population of 100 people. These 100 people can be classified as either ‘Students’ and ‘Teachers’ or as a population of ‘Males’ and ‘Females’.With the table below of the 100 people tabulated in some form, what will be the conditional probability that a certain person of the school is a ‘Student’ given that she is a ‘Female’?FemaleMaleTotalTeacher101020Student305080Total4060100To compute this, you can filter the sub-population of 40 females and focus only on the 30 female students. So the required probability stands as P(Student | Female) = 30/40 = 0.75 .P(Student | Female) = [P(Student ∩ Female)] / [P(Female)] = 30/40 = 0.75This is defined as the intersection(∩) of Student(A) and Female(B) divided by Female(B). Similarly, the conditional probability of B given A can also be calculated using the same mathematical expression.What is Bayes' Theorem?Bayes' Theorem helps you examine the probability of an event based on the prior knowledge of any event that has correspondence to the former event. Its uses are mainly found in probability theory and statistics. The term naive is used in the sense that the features given to the model are not dependent on each other. In simple terms, if you change the value of one feature in the algorithm, it will not directly influence or change the value of the other features.Consider for example the probability that the price of a house is high can be calculated better if we have some prior information like the facilities around it compared to another assessment made without the knowledge of the location of the house. P(A|B) = [P(B|A)P(A)]/[P(B)]The equation above shows the basic representation of the Bayes' theorem where A and B are two events and:P(A|B): The conditional probability that event A occurs, given that B has occurred. This is termed as the posterior probability. P(A) and P(B): The probability of A and B without any correspondence with each other. P(B|A):  The conditional probability of the occurrence of event B, given that A has occurred.Now the question is how you can use Bayes' Theorem in your machine learning models. To understand it clearly, let us take an example. Consider a simple problem where you need to learn a machine learning model from a given set of attributes. Then you will have to describe a hypothesis or a relation to a response variable and then using this relation, you will have to predict a response, given the set of attributes you have. You can create a learner using Bayes' Theorem that can predict the probability of the response variable that will belong to the same class, given a new set of attributes. Consider the previous question again and then assume that A is the response variable and B is the given attribute. So according to the equation of Bayes' Theorem, we have:P(A|B): The conditional probability of the response variable that belongs to a particular value, given the input attributes, also known as the posterior probability.P(A): The prior probability of the response variable.P(B): The probability of training data(input attributes) or the evidence.P(B|A): This is termed as the likelihood of the training data.The Bayes' Theorem can be reformulated in correspondence with the machine learning algorithm as:posterior = (prior x likelihood) / (evidence)Let’s look into another problem. Consider a situation where the number of attributes is n and the response is a Boolean value. i.e. Either True or False. The attributes are categorical (2 categories in this case). You need to train the classifier for all the values in the instance and the response space.This example is practically not possible in most machine learning algorithms since you need to compute 2∗(2^n-1) parameters for learning this model.  This means for 30 boolean attributes, you will need to learn more than 3 billion parameters which is unrealistic.What is a Naive Bayes Classifier?A classifier is a machine learning model which is used to classify different objects based on certain behavior. Naive Bayes classifiers in machine learning are a family of simple probabilistic machine learning models that are based on Bayes' Theorem. In simple words, it is a classification technique with an assumption of independence among predictors.The Naive Bayes classifier reduces the complexity of the Bayesian classifier by making an assumption of conditional dependence over the training dataset.Consider you are given variables X, Y, and Z. X will be conditionally independent of Y given Z if and only if the probability distribution of X is independent of the value of Y given Z. This is the assumption of conditional dependence.In other words, you can also say that X and Y are conditionally independent given Z if and only if, the knowledge of the occurrence of X provides no information on the likelihood of the occurrence of Y and vice versa, given that Z occurs. This assumption is the reason behind the term naive in Naive Bayes.The likelihood can be written considering n different attributes as:                n           P(X₁...Xₙ|Y) = π P(Xᵢ|Y)        i=1In the mathematical expression, X represents the attributes, Y represents the response variable. So, P(X|Y) becomes equal to the product of the probability distribution of each attribute given Y.Maximizing a PosterioriIf you want to find the posterior probability of P(Y|X) for multiple values of Y, you need to calculate the expression for all the different values of Y. Let us assume a new instance variable X_NEW. You need to calculate the probability that Y will take any value given the observed attributes of X_NEW and given the distributions P(Y) and P(X|Y) which are estimated from the training dataset. In order to predict the response variable depending on the different values obtained for P(Y|X), you need to consider a probable value or the maximum of the values. Hence, this method is known as maximizing a posteriori.Maximizing LikelihoodYou can simplify the Naive Bayes algorithm if you assume that the response variable is uniformly distributed which means that it is equally likely to get any response. The advantage of this assumption is that the a priori or the P(Y) becomes a constant value. Since the a priori and the evidence become independent from the response variable, they can be removed from the equation. So, maximizing the posteriori becomes maximizing the likelihood problem.How to make predictions with a Naive Bayes model?Consider a situation where you have 1000 fruits which are either ‘banana’ or ‘apple’ or ‘other’. These will be the possible classes of the variable Y.The data for the following X variables all of which are in binary (0 and 1):Long SweetYellowThe training dataset will look like this:FruitLong (x1)Sweet (x2)Yellow (x3)Apple001Banana101Apple010Other111........Now let us sum up the training dataset to form a count table as below:TypeLongNot LongSweetNot sweetYellowNot YellowTotalBanana40010035015045050500Apple03001501503000300Other1001001505050150200Total5005006503508002001000The main agenda of the classifier is to predict if a given fruit is a ‘Banana’ or an ‘Apple’ or ‘Other’ when the three attributes(long, sweet and yellow) are known.Consider a case where you’re given that a fruit is long, sweet and yellow and you need to predict what type of fruit it is. This case is similar to the case where you need to predict Y only when the X attributes in the training dataset are known. You can easily solve this problem by using Naive Bayes.The thing you need to do is to compute the 3 probabilities,i.e. the probability of being a banana or an apple or other. The one with the highest probability will be your answer. Step 1:First of all, you need to compute the proportion of each fruit class out of all the fruits from the population which is the prior probability of each fruit class. The Prior probability can be calculated from the training dataset:P(Y=Banana) = 500 / 1000 = 0.50P(Y=Apple) = 300 / 1000 = 0.30P(Y=Other) = 200 / 1000 = 0.20The training dataset contains 1000 records. Out of which, you have 500 bananas, 300 apples and 200 others. So the priors are 0.5, 0.3 and 0.2 respectively. Step 2:Secondly, you need to calculate the probability of evidence that goes into the denominator. It is simply the product of P of X’s for all X:P(x1=Long) = 500 / 1000 = 0.50P(x2=Sweet) = 650 / 1000 = 0.65P(x3=Yellow) = 800 / 1000 = 0.80Step 3:The third step is to compute the probability of likelihood of evidence which is nothing but the product of conditional probabilities of the 3 attributes. The Probability of Likelihood for Banana:P(x1=Long | Y=Banana) = 400 / 500 = 0.80P(x2=Sweet | Y=Banana) = 350 / 500 = 0.70P(x3=Yellow | Y=Banana) = 450 / 500 = 0.90Therefore, the overall probability of likelihood for banana will be the product of the above three,i.e. 0.8 * 0.7 * 0.9 = 0.504.Step 4:The last step is to substitute all the 3 equations into the mathematical expression of Naive Bayes to get the probability.P(Banana|Long,Sweet and Yellow)  =   [P(Long|Banana)∗P(Sweet|Banana)∗P(Yellow|Banana) x P(Banana)] /                              [P(Long)∗P(Sweet)∗P(Yellow)]=  0.8∗0.7∗0.9∗0.5/[P(Evidence)] = 0.252/[P(Evidence)]P(Apple|Long,Sweet and Yellow) = 0, because P(Long|Apple) = 0P(Other|Long,Sweet and Yellow) = 0.01875/P(Evidence)In a similar way, you can also compute the probabilities for ‘Apple’ and ‘Other’. The denominator is the same for all cases. Banana gets the highest probability, so that will be considered as the predicted class.What are the types of Naive Bayes classifier?The main types of Naive Bayes classifier are mentioned below:Multinomial Naive Bayes — These types of classifiers are usually used for the problems of document classification.  It checks whether the document belongs to a particular category like sports or technology or political etc and then classifies them accordingly. The predictors used for classification in this technique are the frequency of words present in the document. Complement Naive Bayes — This is basically an adaptation of the multinomial naive bayes that is particularly suited for imbalanced datasets.  Bernoulli Naive Bayes — This classifier is also analogous to multinomial naive bayes but instead of words, the predictors are Boolean values. The parameters used to predict the class variable accepts only yes or no values, for example, if a word occurs in the text or not. Out-of-Core Naive Bayes — This classifier is used to handle cases of large scale classification problems for which the complete training dataset might not fit in the memory. Gaussian Naive Bayes — In a Gaussian Naive Bayes, the predictors take a continuous value assuming that it has been sampled from a Gaussian Distribution. It is also called a Normal Distribution.Since the likelihood of the features is assumed to be Gaussian, the conditional probability will change in the following manner:P(xᵢ|y) = 1/(√2пσ²ᵧ) exp[ –(xᵢ - μᵧ)²/2σ²ᵧ]What are the pros and cons of the Naive Bayes?The naive Bayes algorithm has both its pros and its cons. Pros of Naive Bayes —It is easy and fast to predict the class of the training data set. It performs well in multiclass prediction.It performs better as compared to other models like logistic regression while assuming the independent variables.It requires less training data. It performs better in the case of categorical input variables as compared to numerical variables.Cons of Naive Bayes —The model is not able to make a prediction in situations where the categorical variable has a category that was not observed in the training data set and assigns a 0 (zero) probability to it. This is known as the ‘Zero Frequency’. You can solve this using the Laplace estimation.Since Naive Bayes is considered to be a bad estimator, the probability outputs are not taken seriously.Naive Bayes works on the principle of assumption of independent predictors, but it is practically impossible to get a set of predictors that are completely independent.What is Laplace Correction?When you have a model with a lot of attributes, it is possible that the entire probability might become zero because one of the feature’s values is zero. To overcome this situation, you can increase the count of the variable with zero to a small value like in the numerator so that the overall probability doesn’t come as zero. This type of correction is called the Laplace Correction. Usually, all naive Bayes models use this implementation as a parameter.What are the applications of Naive Bayes? There are a lot of real-life applications of the Naive Bayes classifier, some of which are mentioned below:Real-time prediction — It is a fast and eager machine learning classifier, so it is used for making predictions in real-time. Multi-class prediction — It can predict the probability of multiple classes of the target variable. Text Classification/ Spam Filtering / Sentiment Analysis — They are mostly used in text classification problems because of its multi-class problems and the independence rule. They are used for identifying spam emails and also to identify negative and positive customer sentiments on social platforms. Recommendation Systems — A Recommendation system is built by combining Naive Bayes classifier and Collaborating Filtering. It filters unseen information and predicts whether the user would like a given resource or not using machine learning and data mining techniques. How to build a Naive Bayes Classifier in Python?In Python, the Naive Bayes classifier is implemented in the scikit-learn library. Let us look into an example by importing the standard iris dataset to predict the Species of flowers:# Import packages from sklearn.naive_bayes import GaussianNB from sklearn.model_selection import train_test_split from sklearn.metrics import confusion_matrix import numpy as np import pandas as pd import matplotlib.pyplot as plt import seaborn as sns; sns.set() # Import data training = pd.read_csv('/content/iris_training.csv') test = pd.read_csv('/content/iris_test.csv') # Create the X, Y, Training and Test X_Train = training.drop('Species', axis=1) Y_Train = training.loc[:, 'Species'] X_Test = test.drop('Species', axis=1) Y_Test = test.loc[:, 'Species'] # Init the Gaussian Classifier model = GaussianNB() # Train the model model.fit(X_Train, Y_Train) # Predict Output pred = model.predict(X_Test) # Plot Confusion Matrix mat = confusion_matrix(pred, Y_Test) names = np.unique(pred) sns.heatmap(mat, square=True, annot=True, fmt='d', cbar=False,         xticklabels=names, yticklabels=names) plt.xlabel('Truth') plt.ylabel('Predicted')The output will be as follows:Text(89.18, 0.5, 'Predicted')How to improve a Naive Bayes Model?You can improve the power of a Naive Bayes model by following these tips:Transform variables using transformations like BoxCox and YeoJohnson to make continuous features to normal distribution.Use Laplace Correction for handling zero values in X variables and to predict the class of test data set for zero frequency issues. Check for correlated features and remove the highly correlated ones because they are voted twice in the model and might lead to over inflation.Combine different features to make a new product which makes some intuitive sense. Provide more realistic prior probabilities to the algorithm based on knowledge from business. Use ensemble methods like bagging and boosting to reduce the variance. SummaryLet us see what we have learned so far —Naive Bayes and its typesPros and Cons of Naive BayesApplications of Naive BayesHow a Naive Bayes model makes the predictionCreating a Naive Bayes classifierImproving a Naive Bayes modelNaive Bayes is mostly used in real-world applications like sentiment analysis, spam filtering, recommendation systems, etc. They are extremely fast and easy to implement as compared to other machine learning models. However, the biggest drawback of Naive Bayes is the requirement of predictors to be independent. In most real-life cases, the predictors are dependent in nature which hinders the performance of the classifier.  We have covered most of the topics related to algorithms in our series of machine learning blogs, click here. If you are inspired by the opportunities provided by machine learning, enrol in our  Data Science and Machine Learning Courses for more lucrative career options in this landscape.

What is Naive Bayes in Machine Learning

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What is Naive Bayes in Machine Learning

Naive Bayes is a simple but surprisingly powerful probabilistic machine learning algorithm used for predictive modeling and classification tasks. Some typical applications of Naive Bayes are spam filtering, sentiment prediction, classification of documents, etc. It is a popular algorithm mainly because it can be easily written in code and predictions can be made real quick which in turn increases the scalability of the solution. The Naive Bayes algorithm is traditionally considered the algorithm of choice for practical-based applications mostly in cases where instantaneous responses are required for user’s requests.

It is based on the works of the Rev. Thomas Bayes and hence the name. Before starting off with Naive Bayes, it is important to learn about Bayesian learning, what is ‘Conditional Probability’ and ‘Bayes Rule’.

What is Naive Bayes in Machine Learning

Bayesian learning is a supervised learning technique where the goal is to build a model of the distribution of class labels that have a concrete definition of the target attribute. Naïve Bayes is based on applying Bayes' theorem with the naïve assumption of independence between each and every pair of features.

What is Conditional Probability?

Let us start with the primitives by understanding Conditional Probability with some examples.

Example 1

Consider you have a coin and fair dice. When you flip a coin, there is an equal chance of getting either a head or a tail. So you can say that the probability of getting heads or the probability of getting tails is 50%.

Now if you roll the fair dice, the probability of getting 1 out of the 6 numbers would be 1/6 = 0.166. The probability will also be the same for other numbers on the dice.

Example 2

Consider another example of playing cards. You are asked to pick a card from the deck. Can you guess the probability of getting a king given the card is a heart?

The given condition here is that the card is a heart, so the denominator has to be 13 (there are 13 hearts in a deck of cards) and not 52. Since there is only one king in hearts, so the probability that the card is a king given it is a heart is 1/13 = 0.077.

So when you say the conditional probability of A given B, it refers to the probability of the occurrence of A given that B has already occurred. This is a typical example of conditional probability.

Mathematically, the conditional probability of A given B can be defined as P(A AND B) / P(B).

Example 3

Let us see another slightly complicated example to understand conditional probability better.

Consider a school with a total population of 100 people. These 100 people can be classified as either ‘Students’ and ‘Teachers’ or as a population of ‘Males’ and ‘Females’.

With the table below of the 100 people tabulated in some form, what will be the conditional probability that a certain person of the school is a ‘Student’ given that she is a ‘Female’?


FemaleMaleTotal
Teacher101020
Student305080
Total4060100

To compute this, you can filter the sub-population of 40 females and focus only on the 30 female students. So the required probability stands as P(Student | Female) = 30/40 = 0.75 .

P(Student | Female) = [P(Student ∩ Female)] / [P(Female)= 30/40 = 0.75

This is defined as the intersection(∩) of Student(A) and Female(B) divided by Female(B). Similarly, the conditional probability of B given A can also be calculated using the same mathematical expression.

What is Bayes' Theorem?

Bayes' Theorem helps you examine the probability of an event based on the prior knowledge of any event that has correspondence to the former event. Its uses are mainly found in probability theory and statistics. The term naive is used in the sense that the features given to the model are not dependent on each other. In simple terms, if you change the value of one feature in the algorithm, it will not directly influence or change the value of the other features.

Consider for example the probability that the price of a house is high can be calculated better if we have some prior information like the facilities around it compared to another assessment made without the knowledge of the location of the house. 

P(A|B) = [P(B|A)P(A)]/[P(B)]

The equation above shows the basic representation of the Bayes' theorem where A and B are two events and:

P(A|B): The conditional probability that event A occurs, given that B has occurred. This is termed as the posterior probability. 

P(A) and P(B): The probability of A and B without any correspondence with each other. 

P(B|A):  The conditional probability of the occurrence of event B, given that A has occurred.

Now the question is how you can use Bayes' Theorem in your machine learning models. To understand it clearly, let us take an example. 

Consider a simple problem where you need to learn a machine learning model from a given set of attributes. Then you will have to describe a hypothesis or a relation to a response variable and then using this relation, you will have to predict a response, given the set of attributes you have. 

You can create a learner using Bayes' Theorem that can predict the probability of the response variable that will belong to the same class, given a new set of attributes. 

Consider the previous question again and then assume that A is the response variable and B is the given attribute. So according to the equation of Bayes' Theorem, we have:

P(A|B): The conditional probability of the response variable that belongs to a particular value, given the input attributes, also known as the posterior probability.

P(A): The prior probability of the response variable.

P(B): The probability of training data(input attributes) or the evidence.

P(B|A): This is termed as the likelihood of the training data.

The Bayes' Theorem can be reformulated in correspondence with the machine learning algorithm as:

posterior = (prior x likelihood) / (evidence)

Let’s look into another problem. Consider a situation where the number of attributes is n and the response is a Boolean value. i.e. Either True or False. The attributes are categorical (2 categories in this case). You need to train the classifier for all the values in the instance and the response space.

This example is practically not possible in most machine learning algorithms since you need to compute 2∗(2^n-1) parameters for learning this model.  This means for 30 boolean attributes, you will need to learn more than 3 billion parameters which is unrealistic.

What is a Naive Bayes Classifier?

A classifier is a machine learning model which is used to classify different objects based on certain behavior. Naive Bayes classifiers in machine learning are a family of simple probabilistic machine learning models that are based on Bayes' Theorem. In simple words, it is a classification technique with an assumption of independence among predictors.

The Naive Bayes classifier reduces the complexity of the Bayesian classifier by making an assumption of conditional dependence over the training dataset.

Consider you are given variables X, Y, and Z. X will be conditionally independent of Y given Z if and only if the probability distribution of X is independent of the value of Y given Z. This is the assumption of conditional dependence.

In other words, you can also say that X and Y are conditionally independent given Z if and only if, the knowledge of the occurrence of X provides no information on the likelihood of the occurrence of Y and vice versa, given that Z occurs. This assumption is the reason behind the term naive in Naive Bayes.

The likelihood can be written considering n different attributes as:

                n          
P(X₁...Xₙ|Y) = π P(Xᵢ|Y)
       i=1

In the mathematical expression, X represents the attributes, Y represents the response variable. So, P(X|Y) becomes equal to the product of the probability distribution of each attribute given Y.

Maximizing a Posteriori

If you want to find the posterior probability of P(Y|X) for multiple values of Y, you need to calculate the expression for all the different values of Y. 

Let us assume a new instance variable X_NEW. You need to calculate the probability that Y will take any value given the observed attributes of X_NEW and given the distributions P(Y) and P(X|Y) which are estimated from the training dataset. 

In order to predict the response variable depending on the different values obtained for P(Y|X), you need to consider a probable value or the maximum of the values. Hence, this method is known as maximizing a posteriori.

Maximizing Likelihood

You can simplify the Naive Bayes algorithm if you assume that the response variable is uniformly distributed which means that it is equally likely to get any response. The advantage of this assumption is that the a priori or the P(Y) becomes a constant value. 

Since the a priori and the evidence become independent from the response variable, they can be removed from the equation. So, maximizing the posteriori becomes maximizing the likelihood problem.

How to make predictions with a Naive Bayes model?

Consider a situation where you have 1000 fruits which are either ‘banana’ or ‘apple’ or ‘other’. These will be the possible classes of the variable Y.

The data for the following X variables all of which are in binary (0 and 1):

  • Long 
  • Sweet
  • Yellow

The training dataset will look like this:

FruitLong (x1)Sweet (x2)Yellow (x3)
Apple001
Banana101
Apple010
Other111
........

Now let us sum up the training dataset to form a count table as below:

TypeLongNot LongSweetNot sweetYellowNot YellowTotal
Banana40010035015045050500
Apple03001501503000300
Other1001001505050150200
Total5005006503508002001000

The main agenda of the classifier is to predict if a given fruit is a ‘Banana’ or an ‘Apple’ or ‘Other’ when the three attributes(long, sweet and yellow) are known.

Consider a case where you’re given that a fruit is long, sweet and yellow and you need to predict what type of fruit it is. This case is similar to the case where you need to predict Y only when the X attributes in the training dataset are known. You can easily solve this problem by using Naive Bayes.

The thing you need to do is to compute the 3 probabilities,i.e. the probability of being a banana or an apple or other. The one with the highest probability will be your answer. 

Step 1:

First of all, you need to compute the proportion of each fruit class out of all the fruits from the population which is the prior probability of each fruit class. 

The Prior probability can be calculated from the training dataset:

P(Y=Banana) = 500 / 1000 = 0.50

P(Y=Apple) = 300 / 1000 = 0.30

P(Y=Other) = 200 / 1000 = 0.20

The training dataset contains 1000 records. Out of which, you have 500 bananas, 300 apples and 200 others. So the priors are 0.5, 0.3 and 0.2 respectively. 

Step 2:

Secondly, you need to calculate the probability of evidence that goes into the denominator. It is simply the product of P of X’s for all X:

P(x1=Long) = 500 / 1000 = 0.50

P(x2=Sweet) = 650 / 1000 = 0.65

P(x3=Yellow) = 800 / 1000 = 0.80

Step 3:

The third step is to compute the probability of likelihood of evidence which is nothing but the product of conditional probabilities of the 3 attributes. 

The Probability of Likelihood for Banana:

P(x1=Long | Y=Banana) = 400 / 500 = 0.80

P(x2=Sweet | Y=Banana) = 350 / 500 = 0.70

P(x3=Yellow | Y=Banana) = 450 / 500 = 0.90

Therefore, the overall probability of likelihood for banana will be the product of the above three,i.e. 0.8 * 0.7 * 0.9 = 0.504.

Step 4:

The last step is to substitute all the 3 equations into the mathematical expression of Naive Bayes to get the probability.

P(Banana|Long,Sweet and Yellow)  =   [P(Long|Banana)∗P(Sweet|Banana)∗P(Yellow|Banana) x P(Banana)] /                              [P(Long)∗P(Sweet)∗P(Yellow)]
=  0.8∗0.7∗0.9∗0.5/[P(Evidence)= 0.252/[P(Evidence)]

P(Apple|Long,Sweet and Yellow) = 0, because P(Long|Apple) = 0

P(Other|Long,Sweet and Yellow) = 0.01875/P(Evidence)

In a similar way, you can also compute the probabilities for ‘Apple’ and ‘Other’. The denominator is the same for all cases. 

Banana gets the highest probability, so that will be considered as the predicted class.

What are the types of Naive Bayes classifier?

The main types of Naive Bayes classifier are mentioned below:

  • Multinomial Naive Bayes — These types of classifiers are usually used for the problems of document classification.  It checks whether the document belongs to a particular category like sports or technology or political etc and then classifies them accordingly. The predictors used for classification in this technique are the frequency of words present in the document. 
  • Complement Naive Bayes — This is basically an adaptation of the multinomial naive bayes that is particularly suited for imbalanced datasets.  
  • Bernoulli Naive Bayes — This classifier is also analogous to multinomial naive bayes but instead of words, the predictors are Boolean values. The parameters used to predict the class variable accepts only yes or no values, for example, if a word occurs in the text or not. 
  • Out-of-Core Naive Bayes — This classifier is used to handle cases of large scale classification problems for which the complete training dataset might not fit in the memory. 
  • Gaussian Naive Bayes — In a Gaussian Naive Bayes, the predictors take a continuous value assuming that it has been sampled from a Gaussian Distribution. It is also called a Normal Distribution.

What are the types of Naive Bayes classifier

Since the likelihood of the features is assumed to be Gaussian, the conditional probability will change in the following manner:

P(xᵢ|y) = 1/(√2пσ²ᵧ) exp[ –(xᵢ - μᵧ)²/2σ²ᵧ]

What are the pros and cons of the Naive Bayes?

The naive Bayes algorithm has both its pros and its cons. 

Pros of Naive Bayes —

  • It is easy and fast to predict the class of the training data set. 
  • It performs well in multiclass prediction.
  • It performs better as compared to other models like logistic regression while assuming the independent variables.
  • It requires less training data. 
  • It performs better in the case of categorical input variables as compared to numerical variables.

Cons of Naive Bayes —

  • The model is not able to make a prediction in situations where the categorical variable has a category that was not observed in the training data set and assigns a 0 (zero) probability to it. This is known as the ‘Zero Frequency’. You can solve this using the Laplace estimation.
  • Since Naive Bayes is considered to be a bad estimator, the probability outputs are not taken seriously.
  • Naive Bayes works on the principle of assumption of independent predictors, but it is practically impossible to get a set of predictors that are completely independent.

What is Laplace Correction?

When you have a model with a lot of attributes, it is possible that the entire probability might become zero because one of the feature’s values is zero. To overcome this situation, you can increase the count of the variable with zero to a small value like in the numerator so that the overall probability doesn’t come as zero. 

This type of correction is called the Laplace Correction. Usually, all naive Bayes models use this implementation as a parameter.

What are the applications of Naive Bayes? 

There are a lot of real-life applications of the Naive Bayes classifier, some of which are mentioned below:

  • Real-time prediction — It is a fast and eager machine learning classifier, so it is used for making predictions in real-time. 
  • Multi-class prediction — It can predict the probability of multiple classes of the target variable. 
  • Text Classification/ Spam Filtering / Sentiment Analysis — They are mostly used in text classification problems because of its multi-class problems and the independence rule. They are used for identifying spam emails and also to identify negative and positive customer sentiments on social platforms. 
  • Recommendation Systems — A Recommendation system is built by combining Naive Bayes classifier and Collaborating Filtering. It filters unseen information and predicts whether the user would like a given resource or not using machine learning and data mining techniques. 

How to build a Naive Bayes Classifier in Python?

In Python, the Naive Bayes classifier is implemented in the scikit-learn library. Let us look into an example by importing the standard iris dataset to predict the Species of flowers:

# Import packages
from sklearn.naive_bayes import GaussianNB
from sklearn.model_selection import train_test_split
from sklearn.metrics import confusion_matrix
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns; sns.set()

# Import data
training = pd.read_csv('/content/iris_training.csv')
test = pd.read_csv('/content/iris_test.csv')

# Create the X, Y, Training and Test
X_Train = training.drop('Species', axis=1)
Y_Train = training.loc[:, 'Species']
X_Test = test.drop('Species', axis=1)
Y_Test = test.loc[:, 'Species']

# Init the Gaussian Classifier
model = GaussianNB()

# Train the model
model.fit(X_Train, Y_Train)

# Predict Output
pred = model.predict(X_Test)

# Plot Confusion Matrix
mat = confusion_matrix(pred, Y_Test)
names = np.unique(pred)
sns.heatmap(mat, square=True, annot=True, fmt='d', cbar=False,
        xticklabels=names, yticklabels=names)
plt.xlabel('Truth')
plt.ylabel('Predicted')

The output will be as follows:

Text(89.18, 0.5, 'Predicted')

How to build a Naive Bayes Classifier in Python

How to improve a Naive Bayes Model?

You can improve the power of a Naive Bayes model by following these tips:

  1. Transform variables using transformations like BoxCox and YeoJohnson to make continuous features to normal distribution.
  2. Use Laplace Correction for handling zero values in X variables and to predict the class of test data set for zero frequency issues. 
  3. Check for correlated features and remove the highly correlated ones because they are voted twice in the model and might lead to over inflation.
  4. Combine different features to make a new product which makes some intuitive sense. 
  5. Provide more realistic prior probabilities to the algorithm based on knowledge from business. Use ensemble methods like bagging and boosting to reduce the variance. 

Summary

Let us see what we have learned so far —

  • Naive Bayes and its types
  • Pros and Cons of Naive Bayes
  • Applications of Naive Bayes
  • How a Naive Bayes model makes the prediction
  • Creating a Naive Bayes classifier
  • Improving a Naive Bayes model

Naive Bayes is mostly used in real-world applications like sentiment analysis, spam filtering, recommendation systems, etc. They are extremely fast and easy to implement as compared to other machine learning models. However, the biggest drawback of Naive Bayes is the requirement of predictors to be independent. In most real-life cases, the predictors are dependent in nature which hinders the performance of the classifier.  

We have covered most of the topics related to algorithms in our series of machine learning blogs, click here. If you are inspired by the opportunities provided by machine learning, enrol in our  Data Science and Machine Learning Courses for more lucrative career options in this landscape.

Priyankur

Priyankur Sarkar

Data Science Enthusiast

Priyankur Sarkar loves to play with data and get insightful results out of it, then turn those data insights and results in business growth. He is an electronics engineer with a versatile experience as an individual contributor and leading teams, and has actively worked towards building Machine Learning capabilities for organizations.

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If you are even remotely interested in technology you would have heard of machine learning. In fact machine learning is now a buzzword and there are dozens of articles and research papers dedicated to it.  Machine learning is a technique which makes the machine learn from past experiences. Complex domain problems can be resolved quickly and efficiently using Machine Learning techniques.  We are living in an age where huge amounts of data are produced every second. This explosion of data has led to creation of machine learning models which can be used to analyse data and to benefit businesses.  This article tries to answer a few important concepts related to Machine Learning and informs you about the career path in this prestigious and important domain.What is Machine Learning?So, here’s your introduction to Machine Learning. 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Languages like Python and R are popularly used to develop applications using Machine Learning models and algorithms. Python, being the simplest and most flexible language, is very popular for AI and Machine Learning applications. These languages provide rich support of libraries for implementation of Machine Learning Algorithms. A person who is good in programming can work very efficiently in this domain.Mathematics and StatisticsThe base for Machine Learning is mathematics and statistics. Statistics applied to data help in understanding it in micro detail. Many machine learning models are based on the probability theory and require knowledge of linear algebra, transformations etc. A good understanding of statistics and probability increases the early adoption to Machine Learning domain.Analytical toolsA plethora of analytical tools are available where machine learning models are already implemented and made available for use. Also, these tools are very good for visualization purposes. Tools like IBM Cognos, PowerBI, Tableue etc are important to pursue a career as a  Machine Learning engineer.Machine Learning Algorithms and librariesTo become a master in this domain, one must master the libraries which are provided with various programming languages. The basic understanding of how machine learning algorithms work and are implemented is crucial.Data Modelling for Machine Learning based systemsData lies at the core of any Machine Learning application. So, modelling the data to suit the application of Machine Learning algorithms is an important task. Data modelling experts are the heart of development teams that develop machine learning based systems. SQL based solutions like Oracle, SQL Server, and NoSQL solutions are important for modelling data required for Machine Learning applications. MongoDB, DynamoDB, Riak are some important NOSQL based solutions available to process unstructured data for Machine Learning applications.Other than these skills, there are two other skills that may prove to be beneficial for those planning on a career in the Machine Learning domain:Natural Language processing techniquesFor E-commerce sites, customer feedback is very important and crucial in determining the roadmap of future products. Many customers give reviews for the products that they have used or give suggestions for improvement. These feedbacks and opinions are analyzed to gain more insights about the customers buying habits as well as about the products. This is part of natural language processing using Machine Learning. The likes of Google, Facebook, Twitter are developing machine learning algorithms for Natural Language Processing and are constantly working on improving their solutions. Knowledge of basics of Natural Language Processing techniques and libraries is must in the domain of Machine Learning.Image ProcessingKnowledge of Image and Video processing is very crucial when a solution is required to be developed in the area of security, weather forecasting, crop prediction etc. Machine Learning based solutions are very effective in these domains. Tools like Matlab, Octave, OpenCV are some important tools available to develop Machine Learning based solutions which require image or video processing.ConclusionMachine Learning is a technique to automate the tasks based on past experiences. This is among the most lucrative career choices right now and will continue to remain so in the future. Job opportunities are increasing day by day in this domain. Acquiring the right skills by opting for a proper Machine Learning course is important to grow in this domain. You can have an impressive career trajectory as a machine learning expert, provided you have the right skills and expertise.
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Different types of discrete distributions that use discrete data are: Binomial Distribution Hypergeometric Distribution Geometric Distribution Poisson Distribution Negative Binomial Distribution Multinomial Distribution  Continuous data: It can obtain any value irrespective of bound or limit. Example: weight, height, any trigonometric value, age, etc. Different types of continuous distributions that use continuous data are: Beta distribution Cauchy distribution Exponential distribution Gamma distribution Logistic distribution Weibull distribution Types of Probability Distribution explained Here are some of the popular types of Probability distributions used by data science professionals. (Try all the code using Jupyter Notebook) Normal Distribution: It is also known as Gaussian distribution. It is one of the simplest types of continuous distribution. This probability distribution is symmetrical around its mean value. It also shows that data at close proximity of the mean is frequently occurring, compared to data that is away from it. Here, mean = 0, variance = finite valueHere, you can see 0 at the center is the Normal Distribution for different mean and variance values. Here is a code example showing the use of Normal Distribution: from scipy.stats import norm  import matplotlib.pyplot as mpl  import numpy as np  def normalDist() -> None:      fig, ax = mpl.subplots(1, 1)      mean, var, skew, kurt = norm.stats(moments = 'mvsk')      x = np.linspace(norm.ppf(0.01),  norm.ppf(0.99), 100)      ax.plot(x, norm.pdf(x),          'r-', lw = 5, alpha = 0.6, label = 'norm pdf')      ax.plot(x, norm.cdf(x),          'b-', lw = 5, alpha = 0.6, label = 'norm cdf')      vals = norm.ppf([0.001, 0.5, 0.999])      np.allclose([0.001, 0.5, 0.999], norm.cdf(vals))      r = norm.rvs(size = 1000)      ax.hist(r, normed = True, histtype = 'stepfilled', alpha = 0.2)      ax.legend(loc = 'best', frameon = False)      mpl.show()  normalDist() Output: Bernoulli Distribution: It is the simplest type of probability distribution. It is a particular case of Binomial distribution, where n=1. It means a binomial distribution takes 'n' number of trials, where n > 1 whereas, the Bernoulli distribution takes only a single trial.   Probability Mass Function of a Bernoulli’s Distribution is:  where p = probability of success and q = probability of failureHere is a code example showing the use of Bernoulli Distribution: from scipy.stats import bernoulli  import seaborn as sb    def bernoulliDist():      data_bern = bernoulli.rvs(size=1200, p = 0.7)      ax = sb.distplot(          data_bern,           kde = True,           color = 'g',           hist_kws = {'alpha' : 1},          kde_kws = {'color': 'y', 'lw': 3, 'label': 'KDE'})      ax.set(xlabel = 'Bernouli Values', ylabel = 'Frequency Distribution')  bernoulliDist() Output:Continuous Uniform Distribution: In this type of continuous distribution, all outcomes are equally possible; each variable gets the same probability of hit as a consequence. This symmetric probabilistic distribution has random variables at an equal interval, with the probability of 1/(b-a). Here is a code example showing the use of Uniform Distribution: from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb  def uniformDist():      sb.distplot(random.uniform(size = 1200), hist = True)      mpl.show()  uniformDist() Output: Log-Normal Distribution: A Log-Normal distribution is another type of continuous distribution of logarithmic values that form a normal distribution. We can transform a log-normal distribution into a normal distribution. Here is a code example showing the use of Log-Normal Distribution import matplotlib.pyplot as mpl  def lognormalDist():      muu, sig = 3, 1      s = np.random.lognormal(muu, sig, 1000)      cnt, bins, ignored = mpl.hist(s, 80, normed = True, align ='mid', color = 'y')      x = np.linspace(min(bins), max(bins), 10000)      calc = (np.exp( -(np.log(x) - muu) **2 / (2 * sig**2))             / (x * sig * np.sqrt(2 * np.pi)))      mpl.plot(x, calc, linewidth = 2.5, color = 'g')      mpl.axis('tight')      mpl.show()  lognormalDist() Output: Pareto Distribution: It is one of the most critical types of continuous distribution. The Pareto Distribution is a skewed statistical distribution that uses power-law to describe quality control, scientific, social, geophysical, actuarial, and many other types of observable phenomena. The distribution shows slow or heavy-decaying tails in the plot, where much of the data reside at its extreme end. Here is a code example showing the use of Pareto Distribution – import numpy as np  from matplotlib import pyplot as plt  from scipy.stats import pareto  def paretoDist():      xm = 1.5        alp = [2, 4, 6]       x = np.linspace(0, 4, 800)      output = np.array([pareto.pdf(x, scale = xm, b = a) for a in alp])      plt.plot(x, output.T)      plt.show()  paretoDist() Output:Exponential Distribution: It is a type of continuous distribution that determines the time elapsed between events (in a Poisson process). Let’s suppose, that you have the Poisson distribution model that holds the number of events happening in a given period. We can model the time between each birth using an exponential distribution.Here is a code example showing the use of Pareto Distribution – from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb  def expDist():      sb.distplot(random.exponential(size = 1200), hist = True)      mpl.show()   expDist()Output:Types of the Discrete probability distribution – There are various types of Discrete Probability Distribution a Data science aspirant should know about. Some of them are – Binomial Distribution: It is one of the popular discrete distributions that determine the probability of x success in the 'n' trial. We can use Binomial distribution in situations where we want to extract the probability of SUCCESS or FAILURE from an experiment or survey which went through multiple repetitions. A Binomial distribution holds a fixed number of trials. Also, a binomial event should be independent, and the probability of obtaining failure or success should remain the same. Here is a code example showing the use of Binomial Distribution – from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb    def binomialDist():      sb.distplot(random.normal(loc = 50, scale = 6, size = 1200), hist = False, label = 'normal')      sb.distplot(random.binomial(n = 100, p = 0.6, size = 1200), hist = False, label = 'binomial')      plt.show()    binomialDist() Output:Geometric Distribution: The geometric probability distribution is one of the crucial types of continuous distributions that determine the probability of any event having likelihood ‘p’ and will happen (occur) after 'n' number of Bernoulli trials. Here 'n' is a discrete random variable. In this distribution, the experiment goes on until we encounter either a success or a failure. The experiment does not depend on the number of trials. Here is a code example showing the use of Geometric Distribution – import matplotlib.pyplot as mpl  def probability_to_occur_at(attempt, probability):      return (1-p)**(attempt - 1) * probability  p = 0.3  attempt = 4  attempts_to_show = range(21)[1:]  print('Possibility that this event will occur on the 7th try: ', probability_to_occur_at(attempt, p))  mpl.xlabel('Number of Trials')  mpl.ylabel('Probability of the Event')  barlist = mpl.bar(attempts_to_show, height=[probability_to_occur_at(x, p) for x in attempts_to_show], tick_label=attempts_to_show)  barlist[attempt].set_color('g')  mpl.show() Output:Poisson Distribution: Poisson distribution is one of the popular types of discrete distribution that shows how many times an event has the possibility of occurrence in a specific set of time. We can obtain this by limiting the Bernoulli distribution from 0 to infinity. Data analysts often use the Poisson distributions to comprehend independent events occurring at a steady rate in a given time interval. Here is a code example showing the use of Poisson Distribution from scipy.stats import poisson  import seaborn as sb  import numpy as np  import matplotlib.pyplot as mpl  def poissonDist():       mpl.figure(figsize = (10, 10))      data_binom = poisson.rvs(mu = 3, size = 5000)      ax = sb.distplot(data_binom, kde=True, color = 'g',                       bins=np.arange(data_binom.min(), data_binom.max() + 1),                       kde_kws={'color': 'y', 'lw': 4, 'label': 'KDE'})      ax.set(xlabel = 'Poisson Distribution', ylabel='Data Frequency')      mpl.show()      poissonDist() Output:Multinomial Distribution: A multinomial distribution is another popular type of discrete probability distribution that calculates the outcome of an event having two or more variables. The term multi means more than one. The Binomial distribution is a particular type of multinomial distribution with two possible outcomes - true/false or heads/tails. Here is a code example showing the use of Multinomial Distribution – import numpy as np  import matplotlib.pyplot as mpl  np.random.seed(99)   n = 12                      pvalue = [0.3, 0.46, 0.22]     s = []  p = []     for size in np.logspace(2, 3):      outcomes = np.random.multinomial(n, pvalue, size=int(size))        prob = sum((outcomes[:,0] == 7) & (outcomes[:,1] == 2) & (outcomes[:,2] == 3))/len(outcomes)      p.append(prob)      s.append(int(size))  fig1 = mpl.figure()  mpl.plot(s, p, 'o-')  mpl.plot(s, [0.0248]*len(s), '--r')  mpl.grid()  mpl.xlim(xmin = 0)  mpl.xlabel('Number of Events')  mpl.ylabel('Function p(X = K)') Output:Negative Binomial Distribution: It is also a type of discrete probability distribution for random variables having negative binomial events. It is also known as the Pascal distribution, where the random variable tells us the number of repeated trials produced during a specific number of experiments.  Here is a code example showing the use of Negative Binomial Distribution – import matplotlib.pyplot as mpl   import numpy as np   from scipy.stats import nbinom    x = np.linspace(0, 6, 70)   gr, kr = 0.3, 0.7        g = nbinom.ppf(x, gr, kr)   s = nbinom.pmf(x, gr, kr)   mpl.plot(x, g, "*", x, s, "r--") Output: Apart from these mentioned distribution types, various other types of probability distributions exist that data science professionals can use to extract reliable datasets. In the next topic, we will understand some interconnections & relationships between various types of probability distributions. Relationship between various Probability distributions – It is surprising to see that different types of probability distributions are interconnected. In the chart shown below, the dashed line is for limited connections between two families of distribution, whereas the solid lines show the exact relationship between them in terms of transformation, variable, type, etc. Conclusion  Probability distributions are prevalent among data analysts and data science professionals because of their wide usage. Today, companies and enterprises hire data science professionals in many sectors, namely, computer science, health, insurance, engineering, and even social science, where probability distributions appear as fundamental tools for application. It is essential for Data analysts and data scientists. to know the core of statistics. Probability Distributions perform a requisite role in analyzing data and cooking a dataset to train the algorithms efficiently. If you want to learn more about data science - particularly probability distributions and their uses, check out KnowledgeHut's comprehensive Data science course. 
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Types of Probability Distributions Every Data Scie...

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