# Naive Bayes From Scratch

*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*

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:*

importnumpyas npclass 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

posteriors.append(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 / denominatorfromsklearn.model_selectionimporttrain_test_split

fromsklearnimportdatasetsdef accuracy(y_true, y_pred):

accuracy = np.sum(y_true == y_pred) / len(y_true)

return accuracyX, 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()

nb.fit(X_train, y_train)

predictions = nb.predict(X_train)

accuracy(y_train, predictions)Out:

0.92025predictions = nb.predict(X_test)

accuracy(y_test, predictions)Out:

0.921

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*For complete code implementation:*