文档介绍：贝叶斯分类器
□每个记录用一个〃维特征向量X=(xp兀2，…，%d)表示口假定有£个类yvyy...,yk.
给定X，X属于”类的后验概率P(刃X)满足贝叶斯(Bayes)定理
P(X\y)P(y)
"22
□MAP(maxi=P（有房二否INo）xP（婚姻状况二已婚INo）xP（年收入二$120KINo）
=4/7x4/=
P（XIYes）=P（有房二否lYes）xP（婚姻状况二已婚lYes）xP（年收入=$120KIYes）
=-9=0
口计算F(XINo)P(No)和户(XIYes)P(Yes)
P(XINo)P(No)==
P(XIYes)P(Yes)==0
贝叶斯分类器
□问题
口如果诸条件概率尸（X尸无Iy=v.）中的一^为o,贝I］它们的乘积（计算F（XIY利）能表达式）为0
口很可能每个F（X丫二号）都为0
口解决方法
口使用m估计、Laplace估计：
原估计:P（Xj=xi\Y=yj）=叫/rij
m-estimate:P(xIy7)=
nc+mp
n+m
知+1
rij+k
Laplace:P(XZ=xf\Y=y{)=
ExampleofNaiveBayesClassifier
P128数据
Namehuman
GiveBirth
yes
CanFlyno
LiveinWaterno
HaveLegs
yes
Class
mammals
python
rp
no
no
no
non-mammals
salmon
bo
rio
yes
no
non-mammals
whale
yes
np
yes
no
mammals
frog
no
ho
sometimes
yes
non-mammals
komodo
hb
rio
ho
yes
non-mammals
bat
yes
yes
no
yes
mammals
pigeon
no
yes
ho
yes
non-mammals
cat
yes
ho
no
yes
mammals
leopardshark
yes
no
yes
no
non-mammals
turtle
bo
rio
sometimes
yes
non-mammals
penguin
no
ho
sometimes
yes
non-mammals
porcupine
yes
no
no
yes
mammals
eel
bo
rio
yes
no
non-mammals
salamander
no
np
sometimes
yes
non-mammals
gilamonster
no
ho
ho
yes
non-mammals
platypus
hb
rio
ho
yes
mammals
owl
no
yes
no
yes
non-mammals
dolphin
yes
hb
yes
no
mammals
eagle
no
yes
no
yes
non-mammals
GiveBirth
yes
CanFly
no
LiveinWater
yes
HaveLegs
no
Class?
■
A:attributes
M:mammals
N:non-mammals
P(AIM)=-x-x?x-=
7777
11034
P(AI7V)=—x—x—x—=
13131313
7
P(AIM)P(M)=—=
20
13
P(AIN)P(N)=—=
20
P(AIM)P(M)>P(AIN)P(N)
二〉Mammals
P128数据
Namehuman
GiveBirth
yes
CanFlyno
LiveinWaterno
HaveLegs
yes
Class
mammals
python
rp
no
no
no
non-mammals
salmon
bo
rio
yes
no
non-mammals
whale
yes
np
yes
no
mammals
frog
no
ho
sometimes
yes
non-mammals
komodo
hb
rio
ho
yes
non-m