（代码在最下面）
正在学习人工智能课程，作业要求自己写一个贝叶斯分类器，分享一下，一起学习
题目描述：
对于Wine数据库，用Python实现以下内容：
1）利用非参数密度估计方法估计先验概率密度。
2）建立最小错误率Bayes分类器。
3）检验分类器性能。
实验内容及数学原理：
（1）利用非参数密度估计方法估计先验概率密度。
设样本类型为Y，样本有Ck种类别，k=1,2,3
非参数密度估计先验概率为：
P（Y=Ck）=N（yi=ck）/N，k=1,2,3
∴先验概率P（Y=Ck）=样本中Ck的数目/样本总数，k=1,2,3
∴P（Y='1'）=N1/N总
P（Y='2'）=N2/N总
P（Y='3'）=N3/N总
（2）建立最小错误率Bayes分类器。
已知输入变量X={x1,x2,x3，…,x13}
∵xi∈{x1,x2,…,x13}为独立同分布概率
∴联合概率密度P（x1,x2,…,x13）=P（x1）P（x2）…P（x13）
又已知先验概率P（Y=Ck） k=1,2,3
∴后验概率为P（Y=Ck|X）=P（X|Y=Ck）P（Y=Ck）/∑P（X|Y=Ck）P（Y=Ck）
即P（Y=Ck|X）=P(i=1,2…,13)P（xi|Y=Ck）* P（Y=Ck）/∑P（X|Y=Ck）P（Y=Ck）
又假设xi的分布服从一维正态分布
∴需要根据样本数据估计十三个特征的正态分布的参数μ，sˆ2
μi=`xi i=1,2,3…,13
sˆ2= E(x-μ)ˆ2
得到条件概率密度函数P（Xi|Y=Ck），k=1,2,3
∵P(xi)是P（X）的边缘密度概率分布
正态分布的联合概率分布仍为正态分布
∴从而得到后验概率
P（Y=Ck|X）=P P（xi|Y=Ck）*P（Y=Ck）/ P（X） ,k=1,2,3
又因为分母都相同，所以只需判断分子P(i=1,2…,13)P（xi|Y=Ck）* P（Y=Ck）
∴通过判别一个输入X的
MAX=max{
PP（xi|Y=C1）* P（Y=C1），
PP（xi|Y=C2）* P（Y=C2），
PP（xi|Y=C3）* P（Y=C3） }
若 MAX=PP（xi|Y=C1）*P（Y=C1）,则X为C1类
若 MAX=PP（xi|Y=C2）*P（Y=C2）,则X为C2类
若 MAX=PP（xi|Y=C3）*P（Y=C3）,则X为C3类
（3）检验分类器性能。
采用0-1损失函数，对数据集进行K折交叉验证，划分为K个不相交的子集，每次选取K-1个子集进行训练，其余1个子集进行验证，得到测试准确率Rtest。重复K次，计算Rtest的均值，即为正确率。
python代码实现（有注释说明）：
# Load libraries
import pandas
import numpy as np
import scipy.stats as stats
import matplotlib.pyplot as plt
from sklearn import model_selection # 模型比较和选择包
from sklearn.naive_bayes import GaussianNB
class Bayes_Test():
# 读取样本 数据集
def load_dataset(self):
url = 'wine.data'
names = ['class', 'Al', 'Ma', 'Ash', 'Aoa', 'Mag', 'Top', 'Fl', 'No',
'Pr', 'Co', 'Hue', 'OD', 'Pro']
dataset = pandas.read_csv(url, names=names)
return dataset
# 提取样本特征集和类别集 划分训练/测试集
def split_out_dataset(self, dataset):
array = dataset.values # 将数据库转换成数组形式
X = array[:, 1:14].astype(float) # 取特征数值列
Y = array[:, 0] # 取类别列
validation_size = 0.20 # 验证集规模
seed = 7
# 分割数据集 测试/验证
X_train, X_validation, Y_train, Y_validation = \
model_selection.train_test_split(X, Y, test_size=validation_size, random_state=seed)
return X_train, X_validation, Y_train, Y_validation
"""第一步：划分样本集"""
# 提取样本 特征
def split_out_attributes(self, X, Y):
# 提取 每个类别的不同特征
# c1 第一类的特征数组
c1_1 = c1_2 = c1_3 = c1_4 = c1_5 = c1_6 = c1_7 = c1_8 = c1_9 = c1_10 = c1_11 = c1_12 = c1_13 = []
c2_1 = c2_2 = c2_3 = c2_4 = c2_5 = c2_6 = c2_7 = c2_8 = c2_9 = c2_10 = c2_11 = c2_12 = c2_13 = []
c3_1 = c3_2 = c3_3 = c3_4 = c3_5 = c3_6 = c3_7 = c3_8 = c3_9 = c3_10 = c3_11 = c3_12 = c3_13 = []
for i in range(len(Y)):
if (Y[i] == 1):
c1_1.append(X[i, 0])
c1_2.append(X[i, 1])
c1_3.append(X[i, 2])
c1_4.append(X[i, 3])
c1_5.append(X[i, 4])
c1_6.append(X[i, 5])
c1_7.append(X[i, 6])
c1_8.append(X[i, 7])
c1_9.append(X[i, 8])
c1_10.append(X[i, 9])
c1_11.append(X[i, 10])
c1_12.append(X[i, 11])
c1_13.append(X[i, 12])
elif (Y[i] == 2):
# c2 第二类的特征数组
c2_1.append(X[i, 0])
c2_2.append(X[i, 1])
c2_3.append(X[i, 2])
c2_4.append(X[i, 3])
c2_5.append(X[i, 4])
c2_6.append(X[i, 5])
c2_7.append(X[i, 6])
c2_8.append(X[i, 7])
c2_9.append(X[i, 8])
c2_10.append(X[i, 9])
c2_11.append(X[i, 10])
c2_12.append(X[i, 11])
c2_13.append(X[i, 12])
elif (Y[i] == 3):
# c3 第三类的特征数组
c3_1.append(X[i, 0])
c3_2.append(X[i, 1])
c3_3.append(X[i, 2])
c3_4.append(X[i, 3])
c3_5.append(X[i, 4])
c3_6.append(X[i, 5])
c3_7.append(X[i, 6])
c3_8.append(X[i, 7])
c3_9.append(X[i, 8])
c3_10.append(X[i, 9])
c3_11.append(X[i, 10])
c3_12.append(X[i, 11])
c3_13.append(X[i, 12])
else:
pass
return [c1_1, c1_2, c1_3, c1_4, c1_5, c1_6, c1_7, c1_8, c1_9, c1_10, c1_11, c1_12, c1_13,
c2_1, c2_2, c2_3, c2_4, c2_5, c2_6, c2_7, c2_8, c2_9, c2_10, c2_11, c2_12, c2_13,
c3_1, c3_2, c3_3, c3_4, c3_5, c3_6, c3_7, c3_8, c3_9, c3_10, c3_11, c3_12, c3_13]
"""因为符合多变量正态分布，所以需要(μ，∑)两个样本参数"""
"""第二步：计算样本期望μ和样本方差s"""
# 计算样本期望
def cal_mean(self, attributes):
c1_1, c1_2, c1_3, c1_4, c1_5, c1_6, c1_7, c1_8, c1_9, c1_10, c1_11, c1_12, c1_13 \
, c2_1, c2_2, c2_3, c2_4, c2_5, c2_6, c2_7, c2_8, c2_9, c2_10, c2_11, c2_12, c2_13 \
, c3_1, c3_2, c3_3, c3_4, c3_5, c3_6, c3_7, c3_8, c3_9, c3_10, c3_11, c3_12, c3_13 = attributes
# 第一类的期望值μ
e_c1_1 = np.mean(c1_1)
e_c1_2 = np.mean(c1_2)
e_c1_3 = np.mean(c1_3)
e_c1_4 = np.mean(c1_4)
e_c1_5 = np.mean(c1_5)
e_c1_6 = np.mean(c1_6)
e_c1_7 = np.mean(c1_7)
e_c1_8 = np.mean(c1_8)
e_c1_9 = np.mean(c1_9)
e_c1_10 = np.mean(c1_10)
e_c1_11 = np.mean(c1_11)
e_c1_12 = np.mean(c1_12)
e_c1_13 = np.mean(c1_13)
# 第二类的期望值μ
e_c2_1 = np.mean(c2_1)
e_c2_2 = np.mean(c2_2)
e_c2_3 = np.mean(c2_3)
e_c2_4 = np.mean(c2_4)
e_c2_5 = np.mean(c2_5)
e_c2_6 = np.mean(c2_6)
e_c2_7 = np.mean(c2_7)
e_c2_8 = np.mean(c2_8)
e_c2_9 = np.mean(c2_9)
e_c2_10 = np.mean(c2_10)
e_c2_11 = np.mean(c2_11)
e_c2_12 = np.mean(c2_12)
e_c2_13 = np.mean(c2_13)
# 第三类的期望值μ
e_c3_1 = np.mean(c3_1)
e_c3_2 = np.mean(c3_2)
e_c3_3 = np.mean(c3_3)
e_c3_4 = np.mean(c3_4)
e_c3_5 = np.mean(c3_5)
e_c3_6 = np.mean(c3_6)
e_c3_7 = np.mean(c3_7)
e_c3_8 = np.mean(c3_8)
e_c3_9 = np.mean(c3_9)
e_c3_10 = np.mean(c3_10)
e_c3_11 = np.mean(c3_11)
e_c3_12 = np.mean(c3_12)
e_c3_13 = np.mean(c3_13)
return [e_c1_1, e_c1_2, e_c1_3, e_c1_4, e_c1_5, e_c1_6, e_c1_7, e_c1_8, e_c1_9, e_c1_10, e_c1_11, e_c1_12,
e_c1_13,
e_c2_1, e_c2_2, e_c2_3, e_c2_4, e_c2_5, e_c2_6, e_c2_7, e_c2_8, e_c2_9, e_c2_10, e_c2_11, e_c2_12,
e_c2_13,
e_c3_1, e_c3_2, e_c3_3, e_c3_4, e_c3_5, e_c3_6, e_c3_7, e_c3_8, e_c3_9, e_c3_10, e_c3_11, e_c3_12,
e_c3_13]
# 计算样本方差
def cal_var(self, attributes):
c1_1, c1_2, c1_3, c1_4, c1_5, c1_6, c1_7, c1_8, c1_9, c1_10, c1_11, c1_12, c1_13 \
, c2_1, c2_2, c2_3, c2_4, c2_5, c2_6, c2_7, c2_8, c2_9, c2_10, c2_11, c2_12, c2_13 \
, c3_1, c3_2, c3_3, c3_4, c3_5, c3_6, c3_7, c3_8, c3_9, c3_10, c3_11, c3_12, c3_13 = attributes
# 第一类的方差var
var_c1_1 = np.var(c1_1)
var_c1_2 = np.var(c1_2)
var_c1_3 = np.var(c1_3)
var_c1_4 = np.var(c1_4)
var_c1_5 = np.var(c1_5)
var_c1_6 = np.var(c1_6)
var_c1_7 = np.var(c1_7)
var_c1_8 = np.var(c1_8)
var_c1_9 = np.var(c1_9)
var_c1_10 = np.var(c1_10)
var_c1_11 = np.var(c1_11)
var_c1_12 = np.var(c1_12)
var_c1_13 = np.var(c1_13)
# 第二类的方差s
var_c2_1 = np.var(c2_1)
var_c2_2 = np.var(c2_2)
var_c2_3 = np.var(c2_3)
var_c2_4 = np.var(c2_4)
var_c2_5 = np.var(c2_5)
var_c2_6 = np.var(c2_6)
var_c2_7 = np.var(c2_7)
var_c2_8 = np.var(c2_8)
var_c2_9 = np.var(c2_9)
var_c2_10 = np.var(c2_10)
var_c2_11 = np.var(c2_11)
var_c2_12 = np.var(c2_12)
var_c2_13 = np.var(c2_13)
# 第三类的方差s
var_c3_1 = np.var(c3_1)
var_c3_2 = np.var(c3_2)
var_c3_3 = np.var(c3_3)
var_c3_4 = np.var(c3_4)
var_c3_5 = np.var(c3_5)
var_c3_6 = np.var(c3_6)
var_c3_7 = np.var(c3_7)
var_c3_8 = np.var(c3_8)
var_c3_9 = np.var(c3_9)
var_c3_10 = np.var(c3_10)
var_c3_11 = np.var(c3_11)
var_c3_12 = np.var(c3_12)
var_c3_13 = np.var(c3_13)
return [var_c1_1, var_c1_2, var_c1_3, var_c1_4, var_c1_5, var_c1_6, var_c1_7, var_c1_8, var_c1_9, var_c1_10,
var_c1_11, var_c1_12, var_c1_13,
var_c2_1, var_c2_2, var_c2_3, var_c2_4, var_c2_5, var_c2_6, var_c2_7, var_c2_8, var_c2_9, var_c2_10,
var_c2_11, var_c2_12, var_c2_13,
var_c3_1, var_c3_2, var_c3_3, var_c3_4, var_c3_5, var_c3_6, var_c3_7, var_c3_8, var_c3_9, var_c3_10,
var_c3_11, var_c3_12, var_c3_13]
# 计算先验概率P(Y=ck)
def cal_prior_probability(self, Y):
a = b = c = 0
for i in Y:
if (i == 1):
a += 1
elif (i == 2):
b += 1
elif (i == 3):
c += 1
else:
pass
pa = a / len(Y)
pb = b / len(Y)
pc = c / len(Y)
return pa, pb, pc
# 计算后验概率P(Y=ck|X)=P(X|Y=ck)*P(Y=ck)/∑
def cal_posteriori_probability(self, X, Y, p, means, vars):
pa, pb, pc = p
e_c1_1, e_c1_2, e_c1_3, e_c1_4, e_c1_5, e_c1_6, e_c1_7, e_c1_8, e_c1_9, e_c1_10, e_c1_11, e_c1_12, e_c1_13 \
, e_c2_1, e_c2_2, e_c2_3, e_c2_4, e_c2_5, e_c2_6, e_c2_7, e_c2_8, e_c2_9, e_c2_10, e_c2_11, e_c2_12, e_c2_13 \
, e_c3_1, e_c3_2, e_c3_3, e_c3_4, e_c3_5, e_c3_6, e_c3_7, e_c3_8, e_c3_9, e_c3_10, e_c3_11, e_c3_12, e_c3_13 = means
var_c1_1, var_c1_2, var_c1_3, var_c1_4, var_c1_5, var_c1_6, var_c1_7, var_c1_8, var_c1_9, var_c1_10, var_c1_11, var_c1_12, var_c1_13 \
, var_c2_1, var_c2_2, var_c2_3, var_c2_4, var_c2_5, var_c2_6, var_c2_7, var_c2_8, var_c2_9, var_c2_10, var_c2_11, var_c2_12, var_c2_13 \
, var_c3_1, var_c3_2, var_c3_3, var_c3_4, var_c3_5, var_c3_6, var_c3_7, var_c3_8, var_c3_9, var_c3_10, var_c3_11, var_c3_12, var_c3_13 = vars
print('p:', p)
print('means:', means)
print('vars:', vars)
# 分解十三维输入向量X=[X1，X2，X3...X13]为13个一维正态分布函数
X1 = X[:, 0]
X2 = X[:, 1]
X3 = X[:, 2]
X4 = X[:, 3]
X5 = X[:, 4]
X6 = X[:, 5]
X7 = X[:, 6]
X8 = X[:, 7]
X9 = X[:, 8]
X10 = X[:, 9]
X11 = X[:, 10]
X12 = X[:, 11]
X13 = X[:, 12]
# 分类正确数/分类错误数=>计算正确率
true_test = 0
false_test = 0
# 遍历训练整个输入空间，计算后验概率并判决
for i in range(len(X1)):
# 计算后验概率=P(X|Y=C1)P(Y=C1)
P_1 = stats.norm.pdf(
X1[i], e_c1_1, var_c1_1) * stats.norm.pdf(
X2[i], e_c1_2, var_c1_2) * stats.norm.pdf(
X3[i], e_c1_3, var_c1_3) * stats.norm.pdf(
X4[i], e_c1_4, var_c1_4) * stats.norm.pdf(
X5[i], e_c1_5, var_c1_5) * stats.norm.pdf(
X6[i], e_c1_6, var_c1_6) * stats.norm.pdf(
X7[i], e_c1_7, var_c1_7) * stats.norm.pdf(
X8[i], e_c1_8, var_c1_8) * stats.norm.pdf(
X9[i], e_c1_9, var_c1_9) * stats.norm.pdf(
X10[i], e_c1_10, var_c1_10) * stats.norm.pdf(
X11[i], e_c1_11, var_c1_11) * stats.norm.pdf(
X12[i], e_c1_12, var_c1_12) * stats.norm.pdf(
X13[i], e_c1_13, var_c1_13) * pa
# 计算后验概率=P(X|Y=C2)P(Y=C2)
P_2 = stats.norm.pdf(
X1[i], e_c2_1, var_c2_1) * stats.norm.pdf(
X2[i], e_c2_2, var_c2_2) * stats.norm.pdf(
X3[i], e_c2_3, var_c2_3) * stats.norm.pdf(
X4[i], e_c2_4, var_c2_4) * stats.norm.pdf(
X5[i], e_c2_5, var_c2_5) * stats.norm.pdf(
X6[i], e_c2_6, var_c2_6) * stats.norm.pdf(
X7[i], e_c2_7, var_c2_7) * stats.norm.pdf(
X8[i], e_c2_8, var_c2_8) * stats.norm.pdf(
X9[i], e_c2_9, var_c2_9) * stats.norm.pdf(
X10[i], e_c2_10, var_c2_10) * stats.norm.pdf(
X11[i], e_c2_11, var_c2_11) * stats.norm.pdf(
X12[i], e_c2_12, var_c2_12) * stats.norm.pdf(
X13[i], e_c2_13, var_c2_13) * pb
# 计算后验概率=P(X|Y=C3)P(Y=C3)
P_3 = stats.norm.pdf(
X1[i], e_c3_1, var_c3_1) * stats.norm.pdf(
X2[i], e_c3_2, var_c3_2) * stats.norm.pdf(
X3[i], e_c3_3, var_c3_3) * stats.norm.pdf(
X4[i], e_c3_4, var_c3_4) * stats.norm.pdf(
X5[i], e_c3_5, var_c3_5) * stats.norm.pdf(
X6[i], e_c3_6, var_c3_6) * stats.norm.pdf(
X7[i], e_c3_7, var_c3_7) * stats.norm.pdf(
X8[i], e_c3_8, var_c3_8) * stats.norm.pdf(
X9[i], e_c3_9, var_c3_9) * stats.norm.pdf(
X10[i], e_c3_10, var_c3_10) * stats.norm.pdf(
X11[i], e_c3_11, var_c3_11) * stats.norm.pdf(
X12[i], e_c3_12, var_c3_12) * stats.norm.pdf(
X13[i], e_c3_13, var_c3_13) * pc
# 计算判别函数，选取概率最大的类
max_P = max(P_1, P_2, P_3)
# 输出分类结果，并检测正确率
if (max_P == P_1):
if (Y[i] == 1):
print('分为第一类，正确')
true_test += 1
else:
print('分为第一类，错误')
false_test += 1
elif (max_P == P_2):
if (Y[i] == 2):
print('分为第二类，正确')
true_test += 1
else:
print('分为第二类，错误')
false_test += 1
elif (max_P == P_3):
if (Y[i] == 3):
print('分为第三类，正确')
true_test += 1
else:
print('分为第三类，错误')
false_test += 1
else:
print('未分类')
false_test += 1
# 打印分类正确率
print('训练正确率为:', (true_test / (true_test + false_test)))
# 模板方法对照
def cal_dataset(self, X_train, Y_train):
# Test options and evaluation metric
seed = 7
scoring = 'accuracy'
# Check Algorithms
model = GaussianNB()
name = 'bayes classifier'
# 建立K折交叉验证 10倍
kfold = model_selection.KFold(n_splits=10, random_state=seed)
# cross_val_score() 对数据集进行指定次数的交叉验证并为每次验证效果评测
cv_results = \
model_selection.cross_val_score(model, X_train, Y_train, cv=kfold, scoring=scoring)
results = cv_results
msg = "%s: %f (%f)" % (name + '精度', cv_results.mean(), cv_results.std())
print(msg)
# Show Algorithms
dataresult = pandas.DataFrame(results)
dataresult.plot(title='Bayes accuracy analysis', kind='density', subplots=True, layout=(1, 1), sharex=False,
sharey=False)
dataresult.hist()
plt.show()
bayes = Bayes_Test()
dataset = bayes.load_dataset()
# 划分训练集 测试集
X_train, X_validation, Y_train, Y_validation = bayes.split_out_dataset(dataset)
print('得到的X_train', X_train)
print('得到的Y_train', Y_train)
# 分割属性--训练集
attributes = bayes.split_out_attributes(X_train, Y_train)
print('得到的训练集', attributes)
# 计算期望--训练集
means = bayes.cal_mean(attributes)
print('得到的means', means)
# 计算方差--训练集
vars = bayes.cal_var(attributes)
print('得到的vars', vars)
# 计算先验概率--训练集
prior_p = bayes.cal_prior_probability(Y_train)
# 验证分类准确性--测试集
bayes.cal_posteriori_probability(X_train, Y_train, prior_p, means, vars)
# 模板方法--性能对比
bayes.cal_dataset(X_validation,Y_validation)
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