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FAQ /
FinalWhat is Question 6 (Bayes-ed Logic) asking for, specifically?Question 6 wants you to specific the parameters of the Naive Bayes model such that the NB decision rule $Y = \arg\max_y P(Y=y|X_1,\dots,X_n)$ is the same as various logical functions. For example, for the AND function, you want: $$P(Y = 1 | X_1 = 1,\dots,X_n = 1) → P(Y = 0| X_1 = 1, \dots, X_n)$$ but also, $$P(Y = 1 |\dots, X_i = 0, \dots) ← P(Y = 0 | \dots, X_i = 0, \dots),$$ in other words, the probability $P(Y=1|X_i=0,\dots)$ is all assignments where any $X_i$ is equal to zero, regardless. That way, the decision rule is $$Y = \arg\max_y P(Y=y|X_1 = x_1,\dots,X_n=x_n) = \begin{cases} 1 & \textrm{if all} X_i = 1 \\ 0 & \textrm{otherwise} \end{cases}$$ So you have to choose the NB parameters $P(X_i = x_i | Y = y)$ to ensure that this is the case. |