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unit 4/03_Bayesian_Classification.md

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+# Bayesian Classification
+
+**Bayesian Classifiers** are based on probability (Bayes' Theorem). They predict the likelihood that a tuple belongs to a class.
+
+## Bayes' Theorem
+$$ P(H|X) = \frac{P(X|H) \cdot P(H)}{P(X)} $$
+- **P(H|X)**: Posterior Probability (Probability of Hypothesis H given Evidence X).
+- **P(H)**: Prior Probability (Probability of H being true generally).
+- **P(X|H)**: Likelihood (Probability of seeing Evidence X if H is true).
+- **P(X)**: Evidence (Probability of X occurring).
+
+## Naive Bayes Classifier
+- **"Naive"**: It assumes that all attributes are **independent** of each other.
+  - *Example*: It assumes "Income" and "Age" don't affect each other, which simplifies the math.
+- **Pros**: Very fast and effective for large datasets (like spam filtering).
+- **Cons**: The independence assumption is often not true in real life.
+
+## Bayesian Belief Networks (BBN)
+- Unlike Naive Bayes, BBNs **allow** dependencies between variables.
+- They use a graph structure (DAG) to show which variables affect others.