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### Prediction Based on Bayes’ Theorem

- Given training data
**X***, posteriori probability of a hypothesis*H*,*P(H|**X**)*,*follows the Bayes’ theorem

\[P(H|X)=\frac{P(X|H)P(H)}{P(X)}=P(X|H)\times P(H)/P(X)\]

- Informally, this can be viewed as
- posteriori = likelihood x prior/evidence
- Predicts
**X**belongs to Ci iff the probability P(Ci|**X**) is the highest among all the P(Ck|X) for all the*k*classes - Practical difficulty: It requires initial knowledge of many probabilities, involving significant computational cost

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