Use the conditional probabilities in part (a) to predict the class label for a test sample (A = 1, B = 1, C = 1) using the na ??ve Bayes approach.
Consider the data set shown in Table 5.2.
Let R : (A = 1, B = 1, C = 1) be the test record. To determine its
class, we need to compute P(+|R) and P(?|R). Using Bayes theorem,
P(+|R) = P(R|+)P(+)/P(R) and P(?|R) = P(R|?)P(?)/P(R).
Since P(+) = P(?)=0.5 and P(R) is constant, R can be classified by
comparing P(+|R) and P(?|R).
For this question,
P(R|+) = P(A = 1|+) × P(B = 1|+) × P(C = 1|+) = 0.192
P(R|?) = P(A = 1|?) × P(B = 1|?) × P(C = 1|?)=0.032
Since P(R|+) is larger, the record is assigned to (+) class.
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