Naive Bayes

medium· Machine Learningruns: 0

Implement a Gaussian Naive Bayes classifier from scratch. For each class, fit the mean and variance of every feature. Classify by computing the log posterior using the Gaussian likelihood and the class prior, then return the class with the highest posterior.

wpm 0acc 100%time 0:000 / 997

import numpy as np

class GaussianNB:
    def fit(self, X, y):
        self.classes = np.unique(y)
        self.means = {}
        self.vars = {}
        self.priors = {}
        for c in self.classes:
            Xc = X[y == c]
            self.means[c] = Xc.mean(axis=0)
            self.vars[c] = Xc.var(axis=0) + 1e-9
            self.priors[c] = len(Xc) / len(X)

    def _log_likelihood(self, x, c):
        mean = self.means[c]
        var = self.vars[c]
        log_prob = -0.5 * np.sum(np.log(2 * np.pi * var))
        log_prob -= 0.5 * np.sum((x - mean) ** 2 / var)
        return log_prob

    def predict(self, X):
        predictions = []
        for x in X:
            posteriors = []
            for c in self.classes:
                prior = np.log(self.priors[c])
                likelihood = self._log_likelihood(x, c)
                posteriors.append(prior + likelihood)
            predictions.append(self.classes[np.argmax(posteriors)])
        return np.array(predictions)

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