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Unit 3: Classification & Regression

20252m

Naive Bayes assumes
(i) Features are dependent
(ii) Features are independent given the class
(iii) Class probabilities are equal
(iv) No prior knowledge is required

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Answer: (ii) Features are independent given the class

Explanation:

Naive Bayes uses: P(Ck∣x)∝P(Ck)∏i=1nP(xi∣Ck)P(C_k|x) \propto P(C_k)\prod_{i=1}^n P(x_i|C_k)

Naive assumption: xi⊥xj∣Cx_i \perp x_j | C, i.e., features conditionally independent given class label. This drastically reduces parameters from O(2n)O(2^n) to O(n)O(n).

  • (i) dependent — opposite of assumption
  • (iii) class probabilities equal (P(Ck)=1/KP(C_k)=1/K) — not assumed; priors estimated from data P(Ck)=Nk/NP(C_k)=N_k/N
  • (iv) no prior — false; needs P(Ck)P(C_k) (estimated or uniform)

Therefore (ii) is correct. The independence is "naive" because in reality features often correlate, but model still works well in practice.

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