本文仅为了个人学习理解使用
朴素贝叶斯分类器（是一种分类方法）
贝叶斯公式
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P(A mid B)=frac{P(A,B) }{P(B)}=frac{P(B mid A) P(A)}{P(B)}
P(A∣B)=P(B)P(A,B)=P(B)P(B∣A)P(A)
其中：
P
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P(A)
P(A):先验概率
P
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P(A mid B)
P(A∣B):后验概率
P
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P(B mid A)
P(B∣A):在事件A发生的条件下B发生的概率，即似然函数
P
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P(B)
P(B):对于所有类标记都相同，所以证据因子
P
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P(B)
P(B)与类标记无关
P
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Pleft(A_{i} mid Bright)=frac{Pleft(B mid A_{i}right) Pleft(A_{i}right)}{sum_{j} Pleft(B mid A_{j}right) Pleft(A_{j}right)}
P(Ai∣B)=∑jP(B∣Aj)P(Aj)P(B∣Ai)P(Ai)
朴素贝叶斯算法（带例题解释）
则贝叶斯公式可以表示为：
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P
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P
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P
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P
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Pleft(y=c_{n} mid x=Xright)=frac{Pleft(x=X, y=c_{n}right)}{P(x=X)}=frac{Pleft(x=X mid y=c_{n}right) Pleft(y=c_{n}right)}{P(x=X)}
P(y=cn∣x=X)=P(x=X)P(x=X,y=cn)=P(x=X)P(x=X∣y=cn)P(y=cn)
假设各个属性相互独立则：
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∏
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Pleft(x=X mid y=c_{n}right)=prod_{i=1}^{m} Pleft(x^{i}=a_{i} mid y=c_{n}right)
P(x=X∣y=cn)=i=1∏mP(xi=ai∣y=cn)
朴素贝叶斯公式：在特征集合
x
x
x的条件下，
y
y
y取不同值的概率。
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P
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P
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Pleft(y=c_{n} mid x=X right)=frac{Pleft(y=c_{n}right) prod_{i=1}^{m} Pleft(x^{i}=a_{i} mid y=c_{n}right)}{P(x=X)}
P(y=cn∣x=X)=P(x=X)P(y=cn)∏i=1mP(xi=ai∣y=cn)
将使得条件概率最大
y
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y作为预测结果：
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argmax
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f(x)=operatorname{argmax}left(frac{Pleft(y=c_{n}right) prod_{c_{n}}^{m} Pleft(x^{i}=a_{i} mid y=c_{n}right)}{P(x=X)}right)
f(x)=argmax(P(x=X)P(y=cn)∏cnmP(xi=ai∣y=cn))
（证据因子与类标记无关）即
p
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p(x=X)
p(x=X)可以省略
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f(x)=arg max _{c_{n}}left(Pleft(y=c_{n}right) prod_{i=1}^{m} Pleft(x^{i}=a_{i} mid y=c_{n}right)right)
f(x)=argcnmax(P(y=cn)i=1∏mP(xi=ai∣y=cn))
P
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Pleft(y=c_{n}right)=frac{sum_{i=1}^{N} Ileft(y=c_{n}right)}{N}, n=1,2, ldots K
P(y=cn)=N∑i=1NI(y=cn),n=1,2,…K
P
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Pleft(x^{i}=a_{j} mid y=c_{n}right)=frac{sum_{i=1}^{N} Ileft(x_{i}^{j}=a_{j} mid y=c_{n}right)}{sum_{i=1}^{N} Ileft(y_{i}=c_{n}right)}
P(xi=aj∣y=cn)=∑i=1NI(yi=cn)∑i=1NI(xij=aj∣y=cn)
朴素贝叶斯算法的代码实例实现（python）
| 价格A | 课时B | 销量C | 价格A | 课时B | 销量C |
|---|---|---|---|---|---|
| 低 | 多 | 高 | 0 | 2 | 2 |
| 高 | 中 | 高 | 2 | 1 | 2 |
| 低 | 少 | 高 | 0 | 0 | 2 |
| 低 | 中 | 低 | 0 | 1 | 0 |
| 中 | 中 | 中 | 1 | 1 | 1 |
| 高 | 多 | 高 | 2 | 2 | 2 |
| 低 | 少 | 中 | 0 | 0 | 1 |
预测价格A=2（高） 课时B=2（多）时销量
from __future__ import division
from numpy import array
def set_data(price, time, sale):
price_number = []
time_number = []
sale_number = []
for i in price:
if i == "低":
price_number.append(0)
elif i == "中":
price_number.append(1)
elif i == "高":
price_number.append(2)
for j in time:
if j == "少":
time_number.append(0)
elif j == "中":
time_number.append(1)
elif j == "多":
time_number.append(2)
for k in sale:
if k == "低":
sale_number.append(0)
elif k == "中":
sale_number.append(1)
elif k == "高":
sale_number.append(2)
return price_number, time_number, sale_number
price = ["低", "高", "低", "低", "中", "高", "低"]
time = ["多", "中", "少", "中", "中", "多", "少"]
sale = ["高", "高", "高", "低", "中", "高", "中"]
price_number, time_number, sale_number = set_data(price, time, sale)
print(price_number, time_number, sale_number)
P
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P
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P
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P(C=0mid x=X) propto P(C=0)P(A=2 mid C=0)P(B=2 mid C=0)
P(C=0∣x=X)∝P(C=0)P(A=2∣C=0)P(B=2∣C=0)
P
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P(C=1mid x=X)propto P(C=1)P(A=2 mid C=1)P(B=2 mid C=1)
P(C=1∣x=X)∝P(C=1)P(A=2∣C=1)P(B=2∣C=1)
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P
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P(C=2mid x=X)propto P(C=2)P(A=2 mid C=2)P(B=2 mid C=2)
P(C=2∣x=X)∝P(C=2)P(A=2∣C=2)P(B=2∣C=2)
from __future__ import division
price_number = [0, 2, 0, 0, 1, 2, 0]
time_number = [2, 1, 0, 1, 1, 2, 0]
sale_number = [2, 2, 2, 0, 1, 2, 1]
exprice_number = 2
extime_number = 2
sale0p = sale_number.count(0)
sale1p = sale_number.count(1)
sale2p = sale_number.count(2)
a0 = 0
a1 = 0
a2 = 0
b0 = 0
b1 = 0
b2 = 0
for i in range(0, len(sale_number)):
if price_number[i] == 2:
if sale_number[i] == 0:
a0 = a0 + 1
elif sale_number[i] == 1:
a1 = a1 + 1
elif sale_number[i] == 2:
a2 = a2 + 1
if time_number[i] == 2:
if sale_number[i] == 0:
b0 = b0 + 1
elif sale_number[i] == 1:
b1 = b1 + 1
elif sale_number[i] == 2:
b2 = b2 + 1
pa0 = a0 / sale0p
pa1 = a1 / sale1p
pa2 = a2 / sale2p
pb0 = b0 / sale0p
pb1 = b1 / sale1p
pb2 = b2 / sale2p
pc0 = sale0p / len(sale_number)
pc1 = sale1p / len(sale_number)
pc2 = sale2p / len(sale_number)
pcc0 = pc0 * pa0 * pb0
pcc1 = pc1 * pa1 * pb1
pcc2 = pc2 * pa2 * pb2
indf = (pcc0, pcc1, pcc2)
print(indf)
max_indf = indf.index(max(indf))
if max_indf == 0:
print('销量低')
elif max_indf == 1:
print('销量中')
elif max_indf == 2:
print('销量高')
引用的博文
朴素贝叶斯分类算法简单实例
朴素贝叶斯算法（带例题解释）
朴素贝叶斯算法的代码实例实现（python）
