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Suppose you are a product manager, you want to classify customer reviews in positive and negative classes. Or As a loan manager, you want to identify which loan applicants are safe or risky? As a healthcare analyst, you want to predict which patients can suffer from diabetes disease. All the examples have the same kind of problem to classify reviews, loan applicants, and patients.
Naive Bayes is the most straightforward and fast classification algorithm, which is suitable for a large chunk of data. Naive Bayes classifier is successfully used in various applications such as spam filtering, text classification, sentiment analysis, and recommender systems. It uses Bayes theorem of probability for prediction of unknown class.
In this tutorial, you are going to learn about all of the following:
 Classification Workflow
 What is Naive Bayes classifier?
 How Naive Bayes classifier works?
 Classifier building in Scikitlearn
 Zero Probability Problem
 It's advantages and disadvantages
To easily run all the example code in this tutorial yourself, you can create a DataLab workbook for free that has Python preinstalled and contains all code samples. For more practice on scikitlearn, check out our Supervised Learning with Scikitlearn course!
Become a ML Scientist
Classification Workflow
Whenever you perform classification, the first step is to understand the problem and identify potential features and label. Features are those characteristics or attributes which affect the results of the label. For example, in the case of a loan distribution, bank managers identify the customer’s occupation, income, age, location, previous loan history, transaction history, and credit score. These characteristics are known as features that help the model classify customers.
The classification has two phases, a learning phase and the evaluation phase. In the learning phase, the classifier trains its model on a given dataset, and in the evaluation phase, it tests the classifier's performance. Performance is evaluated on the basis of various parameters such as accuracy, error, precision, and recall.
What is Naive Bayes Classifier?
Naive Bayes is a statistical classification technique based on Bayes Theorem. It is one of the simplest supervised learning algorithms. Naive Bayes classifier is the fast, accurate and reliable algorithm. Naive Bayes classifiers have high accuracy and speed on large datasets.
Naive Bayes classifier assumes that the effect of a particular feature in a class is independent of other features. For example, a loan applicant is desirable or not depending on his/her income, previous loan and transaction history, age, and location. Even if these features are interdependent, these features are still considered independently. This assumption simplifies computation, and that's why it is considered as naive. This assumption is called class conditional independence.
 P(h): the probability of hypothesis h being true (regardless of the data). This is known as the prior probability of h.
 P(D): the probability of the data (regardless of the hypothesis). This is known as the prior probability.
 P(hD): the probability of hypothesis h given the data D. This is known as posterior probability.
 P(Dh): the probability of data d given that the hypothesis h was true. This is known as posterior probability.
How Naive Bayes Classifier Works?
Let’s understand the working of Naive Bayes through an example. Given an example of weather conditions and playing sports. You need to calculate the probability of playing sports. Now, you need to classify whether players will play or not, based on the weather condition.
First Approach (In case of a single feature)
Naive Bayes classifier calculates the probability of an event in the following steps:
 Step 1: Calculate the prior probability for given class labels
 Step 2: Find Likelihood probability with each attribute for each class
 Step 3: Put these value in Bayes Formula and calculate posterior probability.
 Step 4: See which class has a higher probability, given the input belongs to the higher probability class.
For simplifying prior and posterior probability calculation, you can use the two tables frequency and likelihood tables. Both of these tables will help you to calculate the prior and posterior probability. The Frequency table contains the occurrence of labels for all features. There are two likelihood tables. Likelihood Table 1 is showing prior probabilities of labels and Likelihood Table 2 is showing the posterior probability.
Now suppose you want to calculate the probability of playing when the weather is overcast.
Probability of playing:
P(Yes  Overcast) = P(Overcast  Yes) P(Yes) / P (Overcast) .....................(1)

Calculate Prior Probabilities:
P(Overcast) = 4/14 = 0.29
P(Yes)= 9/14 = 0.64

Calculate Posterior Probabilities:
P(Overcast Yes) = 4/9 = 0.44

Put Prior and Posterior probabilities in equation (1)
P (Yes  Overcast) = 0.44 * 0.64 / 0.29 = 0.98(Higher)
Similarly, you can calculate the probability of not playing:
Probability of not playing:
P(No  Overcast) = P(Overcast  No) P(No) / P (Overcast) .....................(2)

Calculate Prior Probabilities:
P(Overcast) = 4/14 = 0.29
P(No)= 5/14 = 0.36

Calculate Posterior Probabilities:
P(Overcast No) = 0/9 = 0

Put Prior and Posterior probabilities in equation (2)
P (No  Overcast) = 0 * 0.36 / 0.29 = 0
The probability of a 'Yes' class is higher. So you can determine here if the weather is overcast than players will play the sport.
Second Approach (In case of multiple features)
Now suppose you want to calculate the probability of playing when the weather is overcast, and the temperature is mild.
Probability of playing:
P(Play= Yes  Weather=Overcast, Temp=Mild) = P(Weather=Overcast, Temp=Mild  Play= Yes)P(Play=Yes) ..........(1)
P(Weather=Overcast, Temp=Mild  Play= Yes)= P(Overcast Yes) P(Mild Yes) ………..(2)

Calculate Prior Probabilities: P(Yes)= 9/14 = 0.64

Calculate Posterior Probabilities: P(Overcast Yes) = 4/9 = 0.44 P(Mild Yes) = 4/9 = 0.44

Put Posterior probabilities in equation (2) P(Weather=Overcast, Temp=Mild  Play= Yes) = 0.44 * 0.44 = 0.1936(Higher)

Put Prior and Posterior probabilities in equation (1) P(Play= Yes  Weather=Overcast, Temp=Mild) = 0.1936*0.64 = 0.124
Similarly, you can calculate the probability of not playing:
Probability of not playing:
P(Play= No  Weather=Overcast, Temp=Mild) = P(Weather=Overcast, Temp=Mild  Play= No)P(Play=No) ..........(3)
P(Weather=Overcast, Temp=Mild  Play= No)= P(Weather=Overcast Play=No) P(Temp=Mild  Play=No) ………..(4)

Calculate Prior Probabilities: P(No)= 5/14 = 0.36

Calculate Posterior Probabilities: P(Weather=Overcast Play=No) = 0/9 = 0 P(Temp=Mild  Play=No)=2/5=0.4

Put posterior probabilities in equation (4) P(Weather=Overcast, Temp=Mild  Play= No) = 0 * 0.4= 0

Put prior and posterior probabilities in equation (3) P(Play= No  Weather=Overcast, Temp=Mild) = 0*0.36=0
The probability of a 'Yes' class is higher. So you can say here that if the weather is overcast than players will play the sport.
Classifier Building in Scikitlearn
Naive Bayes Classifier with Synthetic Dataset
In the first example, we will generate synthetic data using scikitlearn and train and evaluate the Gaussian Naive Bayes algorithm.
Generating the Dataset
Scikitlearn provides us with a machine learning ecosystem so that you can generate the dataset and evaluate various machine learning algorithms.
In our case, we are creating a dataset with six features, three classes, and 800 samples using the `make_classification` function.
from sklearn.datasets import make_classification
X, y = make_classification(
n_features=6,
n_classes=3,
n_samples=800,
n_informative=2,
random_state=1,
n_clusters_per_class=1,
)
We will use matplotlib.pyplot’s `scatter` function to visualize the dataset.
import matplotlib.pyplot as plt
plt.scatter(X[:, 0], X[:, 1], c=y, marker="*");
As we can observe, there are three types of target labels, and we will be training a multiclass classification model.
Train Test Split
Before we start the training process, we need to split the dataset into training and testing for model evaluation.
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(
X, y, test_size=0.33, random_state=125
)
Model Building and Training
Build a generic Gaussian Naive Bayes and train it on a training dataset. After that, feed a random test sample to the model to get a predicted value.
from sklearn.naive_bayes import GaussianNB
# Build a Gaussian Classifier
model = GaussianNB()
# Model training
model.fit(X_train, y_train)
# Predict Output
predicted = model.predict([X_test[6]])
print("Actual Value:", y_test[6])
print("Predicted Value:", predicted[0])
Both actual and predicted values are the same.
Actual Value: 0
Predicted Value: 0
Model Evaluation
We will not evolve the model on an unseen test dataset. First, we will predict the values for the test dataset and use them to calculate accuracy and F1 score.
from sklearn.metrics import (
accuracy_score,
confusion_matrix,
ConfusionMatrixDisplay,
f1_score,
)
y_pred = model.predict(X_test)
accuray = accuracy_score(y_pred, y_test)
f1 = f1_score(y_pred, y_test, average="weighted")
print("Accuracy:", accuray)
print("F1 Score:", f1)
Our model has performed fairly well with default hyperparameters.
Accuracy: 0.8484848484848485
F1 Score: 0.8491119695890328
To visualize the Confusion matrix, we will use `confusion_matrix` to calculate the true positives and true negatives and `ConfusionMatrixDisplay` to display the confusion matrix with the labels.
labels = [0,1,2]
cm = confusion_matrix(y_test, y_pred, labels=labels)
disp = ConfusionMatrixDisplay(confusion_matrix=cm, display_labels=labels)
disp.plot();
Our model has performed quite well, and we can improve model performance by scaling, preprocessing crossvalidations, and hyperparameter optimization.
Naive Bayes Classifier with Loan Dataset
Let’s train the Naive Bayes Classifier on the real dataset. We will be repeating most of the tasks except for preprocessing and data exploration.
Data Loading
In this example, we will be loading Loan Data from DataLab using the pandas 'read_csv` function.
import pandas as pd
df = pd.read_csv('loan_data.csv')
df.head()
Data Exploration
To understand more about the dataset we will use `.info()`.
 The dataset consists of 14 columns and 9578 rows.
 Apart from “purpose”, columns are either floats or integers.
 Our target column is “not.fully.paid”.
df.info()
RangeIndex: 9578 entries, 0 to 9577
Data columns (total 14 columns):
# Column NonNull Count Dtype
   
0 credit.policy 9578 nonnull int64
1 purpose 9578 nonnull object
2 int.rate 9578 nonnull float64
3 installment 9578 nonnull float64
4 log.annual.inc 9578 nonnull float64
5 dti 9578 nonnull float64
6 fico 9578 nonnull int64
7 days.with.cr.line 9578 nonnull float64
8 revol.bal 9578 nonnull int64
9 revol.util 9578 nonnull float64
10 inq.last.6mths 9578 nonnull int64
11 delinq.2yrs 9578 nonnull int64
12 pub.rec 9578 nonnull int64
13 not.fully.paid 9578 nonnull int64
dtypes: float64(6), int64(7), object(1)
memory usage: 1.0+ MB
In this example, we will be developing a model to predict the customers who have not fully paid the loan. Let’s explore the purpose and target column by using seaborn’s countplot.
import seaborn as sns
import matplotlib.pyplot as plt
sns.countplot(data=df,x='purpose',hue='not.fully.paid')
plt.xticks(rotation=45, ha='right');
Our dataset is an imbalance that will affect the performance of the model. You can check out Resample an Imbalanced Dataset tutorial to get handson experience in handling imbalanced datasets.
Data Processing
We will now convert the ‘purpose’ column from categorical to integer using pandas `get_dummies` function.
pre_df = pd.get_dummies(df,columns=['purpose'],drop_first=True)
pre_df.head()
After that, we will define feature (X) and target (y) variables, and split the dataset into training and testing sets.
from sklearn.model_selection import train_test_split
X = pre_df.drop('not.fully.paid', axis=1)
y = pre_df['not.fully.paid']
X_train, X_test, y_train, y_test = train_test_split(
X, y, test_size=0.33, random_state=125
)
Model Building and Training
Model building and training is quite simple. We will be training a model on a training dataset using default hyperparameters.
from sklearn.naive_bayes import GaussianNB
model = GaussianNB()
model.fit(X_train, y_train);
Model Evaluation
We will use accuracy and f1 score to determine model performance, and it looks like the Gaussian Naive Bayes algorithm has performed quite well.
from sklearn.metrics import (
accuracy_score,
confusion_matrix,
ConfusionMatrixDisplay,
f1_score,
classification_report,
)
y_pred = model.predict(X_test)
accuray = accuracy_score(y_pred, y_test)
f1 = f1_score(y_pred, y_test, average="weighted")
print("Accuracy:", accuray)
print("F1 Score:", f1)
Accuracy: 0.8206263840556786
F1 Score: 0.8686606980013266
Due to the imbalanced nature of the data, we can see that the confusion matrix tells a different story. On a minority target: `not fully paid`, we have more mislabeled.
labels = ["Fully Paid", "Not fully Paid"]
cm = confusion_matrix(y_test, y_pred)
disp = ConfusionMatrixDisplay(confusion_matrix=cm, display_labels=labels)
disp.plot();
If you are facing issues during training or model evaluation, you can check out Naive Bayes Classification Tutorial using Scikitlearn DataLab workbook. It comes with a dataset, source code, and outputs.
Zero Probability Problem
Suppose there is no tuple for a risky loan in the dataset; in this scenario, the posterior probability will be zero, and the model is unable to make a prediction. This problem is known as Zero Probability because the occurrence of the particular class is zero.
The solution for such an issue is the Laplacian correction or Laplace Transformation. Laplacian correction is one of the smoothing techniques. Here, you can assume that the dataset is large enough that adding one row of each class will not make a difference in the estimated probability. This will overcome the issue of probability values to zero.
For Example: Suppose that for the class loan risky, there are 1000 training tuples in the database. In this database, the income column has 0 tuples for low income, 990 tuples for medium income, and 10 tuples for high income. The probabilities of these events, without the Laplacian correction, are 0, 0.990 (from 990/1000), and 0.010 (from 10/1000)
Now, apply Laplacian correction on the given dataset. Let's add 1 more tuple for each incomevalue pair. The probabilities of these events:
Advantages
 It is not only a simple approach but also a fast and accurate method for prediction.
 Naive Bayes has a very low computation cost.
 It can efficiently work on a large dataset.
 It performs well in case of discrete response variable compared to the continuous variable.
 It can be used with multiple class prediction problems.
 It also performs well in the case of text analytics problems.
 When the assumption of independence holds, a Naive Bayes classifier performs better compared to other models like logistic regression.
Disadvantages
 The assumption of independent features. In practice, it is almost impossible that model will get a set of predictors which are entirely independent.
 If there is no training tuple of a particular class, this causes zero posterior probability. In this case, the model is unable to make predictions. This problem is known as Zero Probability/Frequency Problem.
Conclusion
Congratulations, you have made it to the end of this tutorial!
In this tutorial, you learned about Naïve Bayes algorithm, its working, Naive Bayes assumption, issues, implementation, advantages, and disadvantages. Along the road, you have also learned model building and evaluation in scikitlearn for binary and multinomial classes.
Naive Bayes is the most straightforward and potent algorithm. In spite of the significant advances in machine learning in the last couple of years, it has proved its worth. It has been successfully deployed in many applications, from text analytics to recommendation engines.
If you would like to learn more about scikitlearn in Python, take our Supervised Learning with scikitlearn course and check out our ScikitLearn Tutorial: Baseball Analytics Pt 1.
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