1. For a event X, the optimal classifier is The expected loss: oss (− |A)P (A) P (1|B)P (B) P (1|C)P (C) 0.19 l = P 1 + + = 2. To compute decision boundary: Let (1|x) P (− |x) P > 1 ⇒ Get .4 e .6 e0 * 1√2π − 2 x2 > 0 * 1√2π − 2 (x−3)2 ⇒ n(0.4) x /2 ln(0.6) (x ) /2l − 2 > − − 3 2 ⇒ 1.36484496x < Therefore the optimal bayes classifier is To compute Bayes risk, isk in(0.4 (x|1), 0.6 (x| )) dxr = ∫ +∞ −∞ m * P * P − 1 risk 0.6 (x| ) dx .4 (x|1) dx ⇒ = ∫ 1.3648 −∞ * P − 1 + ∫ +∞ 1.3648 0 * P risk 0.0651⇒ = 3. Let (X |1) N (0, ), P (X | ) N (3, ), P (X) 0.4 P (X |1) .6 P (X | )P ~ 1 − 1 ~ 1 = * + 0 * − 1 P (1|X) P (X |1)P (1) / P (X)⇒ = The expected loss is, oss (1|x) (1 P (1|x)) P (x) dx 0.0961l = ∫ +∞ −∞ 2 * P * − * = Empirical loss is 0 4. The analysis is flawed because many assumptions are not sound. Need to elaborate on your analysis of the paper’s argument. 欢迎咨询51作业君
