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Naive Bayes in Python - ML From Scratch 05

Implement the Naive Bayes algorithm, using only built-in Python modules and numpy, and learn about the math behind this popular ML algorithm.


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

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