Naive Bayes From Scratch

Tanvi Penumudy
Jan 17 · 2 min read

In statistics, Naive Bayes classifiers are a family of simple “probabilistic classifiers” based on applying Bayes’ theorem with strong independence assumptions between the features. Source: Wikipedia

Image Source: Machine Learning Mastery

For the conceptual overview of Naive Bayes, refer — A Machine Learning Roadmap to Naive Bayes

We shall now go through the code walkthrough for the implementation of the Naive Bayes algorithm from scratch:

import numpy as np

class NaiveBayes:

def fit(self, X, y):
n_samples, n_features = X.shape
self._classes = np.unique(y)
n_classes = len(self._classes)

# calculate mean, var, and prior for each class
self._mean = np.zeros((n_classes, n_features), dtype=np.float64)
self._var = np.zeros((n_classes, n_features), dtype=np.float64)
self._priors = np.zeros(n_classes, dtype=np.float64)

for idx, c in enumerate(self._classes):
X_c = X[y==c]
self._mean[idx, :] = X_c.mean(axis=0)
self._var[idx, :] = X_c.var(axis=0)
self._priors[idx] = X_c.shape[0] / float(n_samples)

def predict(self, X):
y_pred = [self._predict(x) for x in X]
return np.array(y_pred)

def _predict(self, x):
posteriors = []

# calculate posterior probability for each class
for idx, c in enumerate(self._classes):
prior = np.log(self._priors[idx])
posterior = np.sum(np.log(self._pdf(idx, x)))
posterior = prior + posterior

# return class with highest posterior probability
return self._classes[np.argmax(posteriors)]

def _pdf(self, class_idx, x):
mean = self._mean[class_idx]
var = self._var[class_idx]
numerator = np.exp(- (x-mean)**2 / (2 * var))
denominator = np.sqrt(2 * np.pi * var)
return numerator / denominator
from sklearn.model_selection import train_test_split
from sklearn import datasets
def accuracy(y_true, y_pred):
accuracy = np.sum(y_true == y_pred) / len(y_true)
return accuracy
X, y = datasets.make_classification(n_samples=10000, n_features=10, n_classes=2, random_state=123) X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=123)

nb = NaiveBayes(), y_train)
predictions = nb.predict(X_train)
accuracy(y_train, predictions)
predictions = nb.predict(X_test)
accuracy(y_test, predictions)

Hope you enjoyed and made the most out of this article! Stay tuned for my upcoming blogs! Make sure to CLAP and FOLLOW if you find my content helpful/informative!

For complete code implementation:

Medium is an open platform where 170 million readers come to find insightful and dynamic thinking. Here, expert and undiscovered voices alike dive into the heart of any topic and bring new ideas to the surface. Learn more

Follow the writers, publications, and topics that matter to you, and you’ll see them on your homepage and in your inbox. Explore

If you have a story to tell, knowledge to share, or a perspective to offer — welcome home. It’s easy and free to post your thinking on any topic. Write on Medium

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store