Naive Bayes classifier is a probabilistic machine learning model that’s used to solve classification problems , is actually based on the Bayes theorem.

The Naive Bayes Model is defined as follows :

Implementation :

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import numpy as np
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

class NaiveBayes:
    
    def fit(self , x , y):
        self.classes = np.unique(y)
        self.nbr_classes = len(self.classes)
        
        self.mean = np.zeros((self.nbr_classes , x.shape[1]) , dtype = np.float64)
        self.variance = np.zeros((self.nbr_classes , x.shape[1]) , dtype = np.float64)
        self.probability_of_a_Class = np.zeros(self.nbr_classes , dtype=np.float64)
        
        for index , classValue in enumerate(self.classes):
            class_i = x[classValue == y]
            self.mean[index , :] = class_i.mean(axis = 0)
            self.variance[index , :] = class_i.var(axis = 0)
            self.probability_of_a_Class[index] = float(class_i.shape[0] / y.shape[0])
            
    def predict(self , x):
        y_predicted =  [self.predictOneSample(xi) for xi in x]
        return np.array(y_predicted)
    
    def predictOneSample(self , x):
        probabilities = []
        for index , classValue in enumerate(self.classes):
            probability = np.log(self.probability_of_a_Class[index]) + np.sum(np.log(self.probability_Density_function(index, x)))
            probabilities.append(probability)           
        return self.classes[np.argmax(probabilities)]
    
    def probability_Density_function(self , classIndex , x):
        mean = self.mean[classIndex]
        variance = self.variance[classIndex]
        numerator = np.exp( - (x - mean**2) / (2 * variance**2))
        denominator = np.sqrt(2 * np.pi * variance)
        return numerator / denominator

Testing The Model :

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x , y = make_classification(n_samples=1000 , n_features=10 , n_classes=2 , random_state=0)

x_train , x_test , y_train , y_test = train_test_split(x,y,test_size=0.25)


N_Bayes = NaiveBayes()
N_Bayes.fit(x_train, y_train) 
y_hat = N_Bayes.predict(x_test)

accuracy = accuracy_score(y_test , y_hat)
print("Model Accuarcy : ", accuracy)