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Naïve Bayes is a supervised machine learning algorithm based on applying Bayes’ theorem with strong (naïve) independence assumptions. Despite the simplicity of the algorithm, Naïve Bayes classifiers have been highly effective for various real-world applications, particularly for tasks like text classification, spam detection, and sentiment analysis. ### Working Principle of Naïve Bayes Algorithm At the core of Naïve Bayes lies Bayes’ theorem, which calculates the posterior probability of a hypothesis given the evidence. Bayes' theorem states that: [ P(A | B) = \frac{P(B | A) P(A)}{P(B)} ] Where: * (P(A | B)) is the posterior probability of the class (A) given the features (B), * (P(B | A)) is the likelihood of feature (B) given class (A), * (P(A)) is the prior probability of the class, * (P(B)) is the evidence or total probability of feature (B). In a Naïve Bayes classifier, the features are assumed to be conditionally independent given the class. This simplifies the computation of the likelihood term. Mathematically, this can be written as: [ P(A | B_1, B_2, \dots, B_n) = \frac{P(A) \prod_{i=1}^{n} P(B_i | A)}{P(B_1, B_2, \dots, B_n)} ] Thus, the classifier multiplies the individual conditional probabilities for each feature and the prior probability of the class to predict the most probable class for a given observation. ### Types of __________ _____ ____ _________ __________ _______ __________ _____ _______ _________ ________.
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