ML | Naive Bayes Scratch Implementation using Python

A key concept in probability theory, the Bayes theorem, provides the foundation for the probabilistic classifier known as Naive Bayes. It is a simple yet powerful algorithm that has risen in popularity because of its understanding, simplicity, and ease of implementation. Naive Bayes Algorithm is a popular method for classification applications, especially spam filtering and text classification. In this article, we will learn about Naive Bayes Classifier From Scratch in Python.

What is Naive Bayes?

Naive Bayes is a family of probabilistic machine learning algorithms based on the Bayes Theorem with an assumption of independence among the features. The Naive Bayes classifier assumes that the presence of a feature in a class is not related to any other feature. Naive Bayes is a classification algorithm for binary and multi-class classification problems.

Naive Bayes Theorem

• Based on prior knowledge of conditions that may be related to an event, Bayes theorem describes the probability of the event
• conditional probability can be found this way
• Assume we have a Hypothesis(H) and evidence(E), 
  According to Bayes theorem, the relationship between the probability of the Hypothesis before getting the evidence represented as P(H) and the probability of the hypothesis after getting the evidence represented as P(H|E) is:

P(H|E) = P(E|H)*P(H)/P(E)

• Prior probability = P(H) is the probability before getting the evidence 
  Posterior probability = P(H|E) is the probability after getting evidence
• In general, 

P(class|data) = (P(data|class) * P(class)) / P(data)

Naive Bayes Theorem Example

Assume we have to find the probability of the randomly picked card to be king given that it is a face card. 

There are 4 Kings in a Deck of Cards which implies that

P(King) = 4/52

as all the Kings are face Cards so

P(Face|King) = 1

there are 3 Face Cards in a Suit of 13 cards and there are 4 Suits in total so

P(Face) = 12/52

Therefore, 

P(King|face) = P(face|king)*P(king)/P(face) = 1/3

For Dataset: Download dataset here

Naive Bayes Scratch Implementation using Python

Here we are implementing a Naive Bayes Algorithm using Gaussian distributions. It performs all the necessary steps from data preparation and model training to testing and evaluation.

Importing Libraries

Importing necessary libraries:

• math: for mathematical operations
• random: for random number generation
• pandas: for data manipulation
• numpy: for scientific computing

Python3

import math
import random
import pandas as pd
import numpy as np

Encode Class

The encode_class function converts class labels in the dataset into numeric values. It assigns a unique numeric identifier to each class.

Python3

def encode_class(mydata):
    classes = []
    for i in range(len(mydata)):
        if mydata[i][-1] not in classes:
            classes.append(mydata[i][-1])
    for i in range(len(classes)):
        for j in range(len(mydata)):
            if mydata[j][-1] == classes[i]:
                mydata[j][-1] = i
    return mydata

Data Splitting

The splitting function is used to split the dataset into training and testing sets based on the given ratio.

Python3

def splitting(mydata, ratio):
    train_num = int(len(mydata) * ratio)
    train = []
    test = list(mydata)
    while len(train) < train_num:
        index = random.randrange(len(test))
        train.append(test.pop(index))
    return train, test

Group Data by Class

The groupUnderClass function takes the data and returns a dictionary where each key is a class label and the value is a list of data points belonging to that class.

Python3

def groupUnderClass(mydata):
    data_dict = {}
    for i in range(len(mydata)):
        if mydata[i][-1] not in data_dict:
            data_dict[mydata[i][-1]] = []
        data_dict[mydata[i][-1]].append(mydata[i])
    return data_dict

Calculate Mean and Standard Deviation for Class

The MeanAndStdDev function takes a list of numbers and calculates the mean and standard deviation.

The MeanAndStdDevForClass function takes the data and returns a dictionary where each key is a class label and the value is a list of lists, where each inner list contains the mean and standard deviation for each attribute of the class.

Python3

def MeanAndStdDev(numbers):
    avg = np.mean(numbers)
    stddev = np.std(numbers)
    return avg, stddev

def MeanAndStdDevForClass(mydata):
    info = {}
    data_dict = groupUnderClass(mydata)
    for classValue, instances in data_dict.items():
        info[classValue] = [MeanAndStdDev(attribute) for attribute in zip(*instances)]
    return info

Calculate Gaussian and Class Probabilities

• The calculateGaussianProbability function takes a value, mean, and standard deviation and calculates the probability of the value occurring under a Gaussian distribution with that mean and standard deviation.
• The calculateClassProbabilities function takes the information dictionary and a test data point as arguments. It iterates through each class and calculates the probability of the test data point belonging to that class based on the mean and standard deviation of each attribute for that class.

Python3

def calculateGaussianProbability(x, mean, stdev):
    epsilon = 1e-10
    expo = math.exp(-(math.pow(x - mean, 2) / (2 * math.pow(stdev + epsilon, 2))))
    return (1 / (math.sqrt(2 * math.pi) * (stdev + epsilon))) * expo

def calculateClassProbabilities(info, test):
    probabilities = {}
    for classValue, classSummaries in info.items():
        probabilities[classValue] = 1
        for i in range(len(classSummaries)):
            mean, std_dev = classSummaries[i]
            x = test[i]
            probabilities[classValue] *= calculateGaussianProbability(x, mean, std_dev)
    return probabilities

Prediction for Test Set

• The predict function takes the information dictionary and a test data point as arguments. It calculates the class probabilities and returns the class with the highest probability.
• The getPredictions function takes the information dictionary and the test set as arguments. It iterates through each test data point and predicts its class using the predict function.

Python3

def predict(info, test):
    probabilities = calculateClassProbabilities(info, test)
    bestLabel = max(probabilities, key=probabilities.get)
    return bestLabel

def getPredictions(info, test):
    predictions = [predict(info, instance) for instance in test]
    return predictions

Calculate Accuracy

The accuracy_rate function takes the test set and the predictions as arguments. It compares the predicted classes with the actual classes and calculates the percentage of correctly predicted data points.

Python3

def accuracy_rate(test, predictions):
    correct = sum(1 for i in range(len(test)) if test[i][-1] == predictions[i])
    return (correct / float(len(test))) * 100.0

Load and Preprocess Data

The code then loads the data from a CSV file using pandas and converts it into a list of lists. It then encodes the class labels and converts all attributes to floating-point numbers.

Python3

# Load data using pandas
filename = '/content/diabetes_data.csv'  # Add the correct file path
df = pd.read_csv(filename)
mydata = df.values.tolist()

# Encode classes and convert attributes to float
mydata = encode_class(mydata)
for i in range(len(mydata)):
    for j in range(len(mydata[i]) - 1):
        mydata[i][j] = float(mydata[i][j])

Split Data into Training and Testing Sets

The code splits the data into training and testing sets using a specified ratio. It then trains the model by calculating the mean and standard deviation for each attribute in each class.

Python3

# Split the data into training and testing sets
ratio = 0.7
train_data, test_data = splitting(mydata, ratio)

print('Total number of examples:', len(mydata))
print('Training examples:', len(train_data))
print('Test examples:', len(test_data))

Output:

Total number of examples: 768
Training examples: 537
Test examples: 231

Train and Test the Model

Calculate mean and standard deviation for each attribute within each class for the training set. Finally, it tests the model on the test set and calculates the accuracy.

Python3

# Train the model
info = MeanAndStdDevForClass(train_data)

# Test the model
predictions = getPredictions(info, test_data)
accuracy = accuracy_rate(test_data, predictions)
print('Accuracy of the model:', accuracy)

Output:

Accuracy of the model: 100.0

Conclusion

In summary, Naive Bayes proves to be an efficient and surprisingly simple algorithm that works well for classification tasks. It is a useful tool for machine learning enthusiasts since it is based on Bayes’ theorem and is simple to use and analyze. Naive Bayes Algorithm -Implementation from scratch in Python can yield useful insights and precise predictions for a variety of applications with careful implementation and analysis.

Frequently Asked Question(FAQs)

1. How to implement Naive Bayes from scratch with Python?

Implementing Naive Bayes from scratch in Python involves defining the necessary functions for calculating the probabilities required for Bayes’ theorem. This includes the prior probability of each class, the conditional probability of each feature given a class, and the likelihood of a given class. Once these probabilities are calculated, Bayes’ theorem can be used to classify new data points.

2. How does Naive Bayes Algorithm works?

Naive Bayes is a probabilistic classifier based on Bayes’ theorem, which states that the probability of an event (hypothesis) given evidence can be calculated as the product of the prior probability of the hypothesis and the likelihood of the evidence given the hypothesis, divided by the marginal probability of the evidence. In the context of Naive Bayes, the hypothesis represents the class label, the evidence represents the features of the data point, and the prior and likelihood probabilities are estimated from the training data.

3. What is Naive Bayes?

Naive Bayes is a classification algorithm based on Bayes’ theorem, which is a statistical method for calculating the probability of an event given a set of conditions. In Naive Bayes, the naive assumption is made that the features of the data are independent of each other, which simplifies the calculations.

4. Why is Naive Bayes a popular algorithm?

Naive Bayes is a popular algorithm due to its simplicity, efficiency, and effectiveness. It is often used as a baseline classifier for comparison with other more complex algorithms.

5. When should I use Naive Bayes?

Naive Bayes is a good choice for problems where the features of the data are relatively independent and where the training data is limited. It is also a good choice for problems where the computational cost is a concern.