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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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