波士顿房价预测案例---多元线性回归【机器学习】_多元线性回归:基于线性回归模型的boston房价预测实现。

boston 房价预测

1、介绍

我们采用波士顿房价预测数据集进行回归任务分析。数据集分为训练集和测试集，训练集可用于训练回归模型，测试集需要进行预测。

2、要求

1. 做linear regression，或使用现成的线性回归函数，方法尝试使用Gradient Descent，SGD 以及 ADAM；
2. 比较不同learning rate的结果。例如损失函数曲线图；
3. 比较有无加上regularization的结果；
4. 比较有无否使用 feature scaling的结果。

3、实现方案

code as follows

1、机器学习（LinearRegression）
2、深度学习（待开始）

3.1、数据未处理

"""
Author:cold
Date:2021-04-01
Version:1.0
Info:baseline
"""
from pandas import read_csv
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error
import pandas as pd
from sklearn.preprocessing import StandardScaler


# 加载数据(455)
dataset =read_csv('train_dataset.csv').values


# 划分训练集和测试集
X = dataset[:,0:13]
Y = dataset[:,13]

x_train,x_test,y_train,y_test = train_test_split(X,Y,test_size=0.3)


# 创建线性回归模型
lr = LinearRegression()
# 拟合训练数据
lr.fit(x_train,y_train)
# 得到预测结果
y_test_pred = lr.predict(x_test)
y_train_pred = lr.predict(x_train)


# 计算相应的评测指标
error_test = mean_squared_error(y_test,y_test_pred)
error_train = mean_squared_error(y_train,y_train_pred)
print("训练集误差为：{}，测试集误差为：{}".format(error_train,error_test))


#预测结果
testset =read_csv('test_dataset.csv').values
x_pred = testset[:,1:14]
y_pred = lr.predict(x_pred)
ID = []
for i in range(len(y_pred)):
    ID.append("id_"+str(i+1))
res = pd.DataFrame()
res['ID']=ID
res['value']=y_pred
res.to_csv('res.csv',index=False)
print("res.csv 已生成")
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52

3.2、数据标准化处理

"""
Author:cold
Date:2021-04-04
Version:2.0
Info:baselineStd
"""
from pandas import read_csv
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error
import pandas as pd
from sklearn.preprocessing import StandardScaler


# 加载数据(455)
dataset =read_csv('train_dataset.csv').values


# 划分训练集和测试集（+数据标准化）
X = dataset[:,0:13]
Y = dataset[:,13]
stand = StandardScaler()
X_std=stand.fit_transform(X)
x_train,x_test,y_train,y_test = train_test_split(X_std,Y,test_size=0.3)


# 创建线性回归模型
lr = LinearRegression()
# 拟合训练数据
lr.fit(x_train,y_train)
# 得到预测结果
y_test_pred = lr.predict(x_test)
y_train_pred = lr.predict(x_train)


# 计算相应的评测指标
error_test = mean_squared_error(y_test,y_test_pred)
error_train = mean_squared_error(y_train,y_train_pred)
print("训练集误差为：{}，测试集误差为：{}".format(error_train,error_test))


#预测结果
testset =read_csv('test_dataset.csv').values
x_pred = testset[:,1:14]
y_pred = lr.predict(x_pred)
ID = []
for i in range(len(y_pred)):
    ID.append("id_"+str(i+1))
res = pd.DataFrame()
res['ID']=ID
res['value']=y_pred
res.to_csv('res.csv',index=False)
print("res.csv 已生成")

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54

3.3、数据标准化处理+特征提取

"""
Author:cold
Date:2021-04-04
Version:3.0
Info:baselineSelFeatures
"""
from pandas import read_csv
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error
import pandas as pd
from sklearn.preprocessing import StandardScaler
from sklearn.feature_selection import SelectKBest,f_regression
from matplotlib import pyplot as plt


#字典结果：{提取k个最佳特征，及索引}
def ToBeStdAndSel(X,Y,k):
    stand = StandardScaler()
    X_std = stand.fit_transform(X)
    best = SelectKBest(f_regression, k=k)
    X_best = best.fit_transform(X_std, Y)#A
    best_index = best.get_support()#B AB顺序不能换
    BEST = {}
    BEST['best_index'] = best_index
    BEST['X_best'] = X_best # 等价于 X_std[:,best_index]
    return BEST

#标准化
def ToBeStd(X):
    stand = StandardScaler()
    X_std = stand.fit_transform(X)
    return X_std

# 保存csv
def ToSaveCsv(y_pred):
    ID = []
    for i in range(len(y_pred)):
        ID.append("id_" + str(i + 1))
    res = pd.DataFrame()
    res['ID'] = ID
    res['value'] = y_pred
    res.to_csv('res.csv', index=False)
    print("res.csv 已生成")

#预测
def TryToPredict(testset):
    x_pred = testset[:, 1:14]
    x_pred_best = ToBeStd(x_pred)[:, best_index]
    y_pred = lr.predict(x_pred_best)
    return y_pred


# 加载数据(455)
dataset =read_csv('train_dataset.csv').values
# 划分训练集和测试集（+数据标准化,+特征提取）X--> X_std--> X_best
X = dataset[:,0:13]
Y = dataset[:,13]
BEST = ToBeStdAndSel(X,Y,6)
X_best = BEST['X_best']
best_index = BEST['best_index']

x_train,x_test,y_train,y_test = train_test_split(X_best,Y,test_size=0.3)

# 创建线性回归模型
lr = LinearRegression()
# 拟合训练数据
lr.fit(x_train,y_train)
# 得到预测结果
y_test_pred = lr.predict(x_test)
y_train_pred = lr.predict(x_train)


# 计算相应的评测指标
error_test = mean_squared_error(y_test,y_test_pred)
error_train = mean_squared_error(y_train,y_train_pred)
print("训练集误差为：{}，测试集误差为：{}".format(error_train,error_test))
plt.plot(y_test_pred,'r-',label='predict_value')
plt.plot(y_test,'b-',label='true_value')
plt.legend()
plt.show()

#预测、保存
testset =read_csv('test_dataset.csv').values
y_pred = TryToPredict(testset)
ToSaveCsv(y_pred)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87

3.4、特征可视化

"""
Author:cold
Date:2021-04-04
Version:1.0
Info: Features show
"""
from pandas import read_csv
import matplotlib.pyplot as plt
import math
# 加载数据(455)
dataset =read_csv('train_dataset.csv').values
X = dataset[:,0:13]
Y = dataset[:,13]
#(特征工程)
features = []
for i in read_csv('train_dataset.csv').keys():
    features.append(i)
nums = len(features)-1
columns =3
rows =math.ceil(nums /columns)
plt.figure(figsize=(12,10))

for i in range(nums):
    plt.subplot(rows,columns,i+1)
    plt.plot(X[:,i],Y,'b+')
    plt.title(features[i])
plt.subplots_adjust(hspace=1.5)
plt.show()
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28

4、优化方向

• 数据特征标准化
• 特征提取
• 异常值判断（箱线图）+数据清洗（较之前mean_square_error更低的原因）
• 更换回归模型
• 模型融合
• 尝试深度学习模型