Explain the concept of Naive Bayes classifier. How does it work?

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The Naive Bayes classifier is a supervised machine learning algorithm based on Bayes' Theorem, used primarily for classification tasks. It's called "naive" because it assumes that all features are independent of each other — an assumption that’s rarely true in real life, but the model often performs surprisingly well despite it.

Bayes' Theorem (Simplified):

P(AB)=P(BA)P(A)P(B)P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}

In classification terms:

  • P(A|B) = Probability of class A given the input features B (posterior probability)

  • P(B|A) = Likelihood of observing features B given class A

  • P(A) = Prior probability of class A

  • P(B) = Probability of features B (evidence)

How Naive Bayes Works:

  1. Training Phase:

    • Calculate the prior probability for each class (how frequent each class is in the dataset).

    • For each feature, compute the likelihood of that feature value for each class.

  2. Prediction Phase:

    • Given a new input, use Bayes' Theorem to calculate the posterior probability for each class.

    • Choose the class with the highest posterior probability as the prediction.

Types of Naive Bayes:

  • Gaussian Naive Bayes – for continuous data (assumes normal distribution)

  • Multinomial Naive Bayes – for discrete counts (e.g., word counts in text)

  • Bernoulli Naive Bayes – for binary features

Applications:

  • Spam detection

  • Sentiment analysis

  • Document classification

  • Medical diagnosis

Despite its simplicity, Naive Bayes is fast, scalable, and works well with high-dimensional data, especially in text classification tasks.

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