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Naïve Bayes Classifier: An Example

  • P(Ci): P(buys_computer = “yes”) = 9/14 = 0.643
    P(buys_computer =“no”) = 5/14= 0.357
  • Compute P(X|Ci) for each class
    P(age = “<=30” | buys_computer = “yes”) = 2/9 = 0.222
    P(age = “<= 30” | buys_computer = “no”) = 3/5 = 0.6
    P(income = “medium” | buys_computer = “yes”) = 4/9 = 0.444
    P(income = “medium” | buys_computer = “no”) = 2/5 = 0.4
    P(student = “yes” | buys_computer = “yes) = 6/9 = 0.667
    P(student = “yes” | buys_computer = “no”) = 1/5 = 0.2
    P(credit_rating = “fair” | buys_computer = “yes”) = 6/9 = 0.667
    P(credit_rating = “fair” | buys_computer = “no”) = 2/5 = 0.4
  • X = (age <= 30 , income = medium, student = yes, credit_rating = fair)
    P(X|Ci) : P(X|buys_computer = “yes”) = 0.222 x 0.444 x 0.667 x 0.667 = 0.044
    P(X|buys_computer = “no”) = 0.6 x 0.4 x 0.2 x 0.4 = 0.019
    P(X|Ci)*P(Ci) : P(X|buys_computer = “yes”) * P(buys_computer = “yes”) = 0.028
    P(X|buys_computer = “no”) * P(buys_computer = “no”) = 0.007
    Therefore, X belongs to class (“buys_computer = yes”)

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