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RID age income student credit Ci
: buy
1 youth high no fair C2: no
2 youth high no excellent C2: no
3 middle-aged high no fair C1: yes
4 senior medium no fair C1: yes
5 senior low yes fair C1: yes
6 senior low yes excellent C2: no
7 middle-aged low yes excellent C1: yes
8 youth medium no fair C2: no
9 youth low yes fair C1: yes
10 senior medium yes fair C1: yes
11 youth medium yes excellent C1: yes
12 middle-aged medium no excellent C1: yes
13 middle-aged high yes fair C1: yes
14 senior medium no excellent C2: no
The data samples are described by attributes age, income, student,
and credit. The class label attribute, buy, tells whether the person
buys a computer, has two distinct values, yes (class C1) and no (class
Toc JJ II J I Back J Doc Doc I
Section 3: Example: Using the Naive Bayesian Classifier 10
C2).
The sample we wish to classify is
X = (age = youth, income = medium, student = yes, credit = fair)
We need to maximize P(X|Ci)P(Ci), for i = 1, 2. P(Ci), the a
priori probability of each class, can be estimated based on the training
samples:
P(buy = yes) = 9
14
P(buy = no) = 5
14
To compute P(X|Ci), for i = 1, 2, we compute the following conditional probabilities:
P(age = youth|buy = yes) = 2
9
P(age = youth|buy = no) = 3
5
P(income = medium|buy = yes) = 4
9
Toc JJ II J I Back J Doc Doc I
Section 3: Example: Using the Naive Bayesian Classifier 11
P(income = medium|buy = no) = 2
5
P(student = yes|buy = yes) = 6
9
P(student = yes|buy = no) = 1
5
P(credit = fair|buy = yes) = 6
9
P(credit = fair|buy = no) = 2
5
Using the above probabilities, we obtain
P(X|buy = yes) = P(age = youth|buy = yes)
P(income = medium|buy = yes)
P(student = yes|buy = yes)
P(credit = fair|buy = yes)
=
2
9
4
9
6
9
6
9
= 0.044.
Toc JJ II J I Back J Doc Doc I
Section 3: Example: Using the Naive Bayesian Classifier 12
Similarly,
P(X|buy = no) = 3
5
2
5
1
5
2
5
= 0.019
To find the class that maximizes P(X|Ci)P(Ci), we compute
P(X|buy = yes)P(buy = yes) = 0.028
P(X|buy = no)P(buy = no) = 0.007
Thus the naive Bayesian classifier predicts buy = yes for sample X.
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