In this Machine Learning from Scratch Tutorial, we are going to implement the Naive Bayes algorithm, using only built-in Python modules and numpy. We will also learn about the concept and the math behind this popular ML algorithm.

All algorithms from this course can be found on GitHub together with example tests.

### Further readings:

https://towardsdatascience.com/naive-bayes-classifier-81d512f50a7c

## Implementation

```
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
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 / denominator
```