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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.