朴素贝叶斯(Bayes)算法例题

朴素贝叶斯(Bayes)算法例题

题目给出

1. 待分类的未知样本

   X=(age="<=30",income="M",student="Y",credit_rating="fair")

   求该样本的buys_computer属性值是啥(Y/N)

2. 下表数据

序号	age	income	student	credit_rating	buys_computer
1	<=30	H	N	fair	N
2	<=30	H	N	excellent	N
3	31~40	H	N	fair	Y
4	>40	M	N	fair	Y
5	>40	L	Y	fair	Y
6	>40	L	Y	excellent	N
7	31~40	L	Y	excellent	Y
8	<=30	M	N	fair	N
9	<=30	L	Y	fair	Y
10	>40	M	Y	fair	Y
11	<=30	M	Y	excellent	Y
12	31~40	M	N	excellent	Y
13	31~40	H	Y	fair	Y
14	>40	M	N	excellent	N

解：

1. 由于要求buys_computer属性是啥值，所以先求其属性两种值分别的概率

   P(buys_computer="Y")=9/14=0.643

   P(buys_computer="N")=5/14=0.357

2. 再求出待分类样本X=(age="<=30",income="M",student="Y",credit_rating="fair")

   中各个属性值发生在(buys_computer="Y")和(buys_computer="N")的各个概率：

   • P(age<=30|buys_computer="Y")=2/9=0.222

   • P(age<=30|buys_computer="N")=3/5=0.6

   • P(income="M"|buys_computer="Y")=4/9=0.444

   • P(income="M"|buys_computer="N")=2/5=0.4

   • P(student="Y"|buys_computer="Y")=6/9=0.677

   • P(student="Y"|buys_computer="N")=1/5=0.2

   • P(credit_rating="fair"|buys_computer="Y")=6/9=0.677

   • P(credit_rating="fair"|buys_computer="N")=2/5=0.4

3. 假设条件独立性，使用以上概率，得到:

   • 将上面所有的发生在(buys_computer="Y")的概率相乘

     P(X|buys_computer="Y")=0.222 * 0.444 * 0.677 * 0.677 = 0.044----------①

   • 将上面所有的发生在(buys_computer="N")的概率相乘

     P(X|buys_computer="N")=0.6 * 0.4 * 0.2 * 0.4= 0.019----------②

   • 再将发生在(buys_computer="Y")的概率相乘的结果①乘以(buys_computer="Y")的概率

     P(X|buys_computer="Y") * P(buys_computer="Y") = 0.044 * 0.643 = 0.028-------③

   • 再将发生在(buys_computer="N")的概率相乘的结果②乘以(buys_computer="N")的概率

     P(X|buys_computer="N") * P(buys_computer="N") = 0.019 * 0.357 = 0.007---------④

4. 由于③>④，所以待分类样本X=(age="<=30",income="M",student="Y",credit_rating="fair")的

   buys_computer属性值是Y