机器学习 – 逻辑回归测试通过或失败预测

逻辑回归预测考试是否通过

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注：本篇文章基于sklearn库，这里我们应该掌握的基础知识有：logistic回归。
目标：基于数据集建立逻辑回归模型，给定两个分数，预测第三个分数能否通过；建立二阶边界以提高模型的准确性。

# 加载数据
import pandas as pd
import numpy as np 
data = pd.read_csv('examdata.csv')
data.head()

# 可视化数据 
import matplotlib.pyplot as plt
fig1 = plt.figure()
plt.figure(figsize=(8,8))
plt.scatter(data.loc[:,'Exam1'],data.loc[:,'Exam2'])
plt.title('Exam1 VS Exam2')
plt.xlabel('Exam1')
plt.ylabel('Exam2')
plt.show()

<Figure size 432x288 with 0 Axes>

#添加标签
mask = data.loc[:,'Pass']==1

fig2 = plt.figure()
plt.figure(figsize=(8,8))
passed = plt.scatter(data.loc[:,'Exam1'][mask],data.loc[:,'Exam2'][mask])
failed = plt.scatter(data.loc[:,'Exam1'][~mask],data.loc[:,'Exam2'][~mask])
plt.title('Exam1 VS Exam2')
plt.xlabel('Exam1')
plt.ylabel('Exam2')
plt.legend((passed,failed),('passed','failed'))
plt.show()

# 对变量进行数据赋值
x = data.drop(['Pass'],axis=1)
#x.head()
y = data.loc[:,'Pass']
#y.head()
x1 = data.loc[:,'Exam1']
#x1.head()
x2 = data.loc[:,'Exam2']
#x2.head()

# 建立并训练模型
from sklearn.linear_model import LogisticRegression
LR = LogisticRegression()
LR.fit(x,y)

LogisticRegression()

# 显示预测结果
y_predict = LR.predict(x)
print(y_predict)

[0 0 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1
 1 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1
 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1]

from sklearn.metrics import accuracy_score
accuracy = accuracy_score(y,y_predict)
print(accuracy)

0.89

# 进行结果测试
y_test = LR.predict([[70,65]])
#print(y_test)
print('passed' if y_test==1 else 'failed')

#画出直线
theta0 = LR.intercept_ #截距
theta1,theta2 = LR.coef_[0][0],LR.coef_[0][1]
print(theta0,theta1,theta2)

[-25.05219314] 0.20535491217790372 0.20058380395469036

边界函数为：

x2_new = -(theta0+theta1*x1)/theta2
print(x2_new)

0     89.449169
1     93.889277
2     88.196312
3     63.282281
4     43.983773
        ...    
95    39.421346
96    81.629448
97    23.219064
98    68.240049
99    48.341870
Name: Exam1, Length: 100, dtype: float64

fig3 = plt.figure()
passed = plt.scatter(data.loc[:,'Exam1'][mask],data.loc[:,'Exam2'][mask])
failed = plt.scatter(data.loc[:,'Exam1'][~mask],data.loc[:,'Exam2'][~mask])
plt.plot(x1,x2_new)
plt.title('Exam1 VS Exam2')
plt.xlabel('Exam1')
plt.ylabel('Exam2')
plt.legend((passed,failed),('passed','failed'))
plt.show()

二阶边界函数：

#创建新的数据集
x1_2 = x1*x1
x2_2 = x2*x2
x1_x2 = x1*x2
#print(x1,x1_2)

x_new = {'x1':x1,'x2':x2,'x1_2':x1_2,'x2_2':x2_2,'x1_x2':x1_x2}
x_new = pd.DataFrame(x_new)
print(x_new)

           x1         x2         x1_2         x2_2        x1_x2
0   34.623660  78.024693  1198.797805  6087.852690  2701.500406
1   30.286711  43.894998   917.284849  1926.770807  1329.435094
2   35.847409  72.902198  1285.036716  5314.730478  2613.354893
3   60.182599  86.308552  3621.945269  7449.166166  5194.273015
4   79.032736  75.344376  6246.173368  5676.775061  5954.672216
..        ...        ...          ...          ...          ...
95  83.489163  48.380286  6970.440295  2340.652054  4039.229555
96  42.261701  87.103851  1786.051355  7587.080849  3681.156888
97  99.315009  68.775409  9863.470975  4730.056948  6830.430397
98  55.340018  64.931938  3062.517544  4216.156574  3593.334590
99  74.775893  89.529813  5591.434174  8015.587398  6694.671710

[100 rows x 5 columns]

LR2 = LogisticRegression()
LR2.fit(x_new,y)

LogisticRegression()

y2_predict = LR2.predict(x_new)
accuracy2 = accuracy_score(y,y2_predict)
print(accuracy2)

1.0

LR2.coef_

array([[-8.95942818e-01, -1.40029397e+00, -2.29434572e-04,
         3.93039312e-03,  3.61578676e-02]])

x1_new = x1.sort_values()#排序,原因是让后面画图按照次序画图以防止画图很凌乱无序。
print(x1,x1_new)

0     34.623660
1     30.286711
2     35.847409
3     60.182599
4     79.032736
        ...    
95    83.489163
96    42.261701
97    99.315009
98    55.340018
99    74.775893
Name: Exam1, Length: 100, dtype: float64 63    30.058822
1     30.286711
57    32.577200
70    32.722833
36    33.915500
        ...    
56    97.645634
47    97.771599
51    99.272527
97    99.315009
75    99.827858
Name: Exam1, Length: 100, dtype: float64

theta0 = LR2.intercept_
theta1 = LR2.coef_[0][0]
theta2 = LR2.coef_[0][1]
theta3 = LR2.coef_[0][2]
theta4 = LR2.coef_[0][3]
theta5 = LR2.coef_[0][4]
a = theta4
b = theta2+theta5*x1_new
c = theta0+theta1*x1_new+theta3*x1_new*x1_new

x2_new_boundary = (-b+(np.sqrt(b*b-4*a*c)))/(2*a)
plt.plot(x1_new,x2_new_boundary)

[<matplotlib.lines.Line2D at 0x1ce77b30b50>]

fig4 = plt.figure()
passed = plt.scatter(data.loc[:,'Exam1'][mask],data.loc[:,'Exam2'][mask])
failed = plt.scatter(data.loc[:,'Exam1'][~mask],data.loc[:,'Exam2'][~mask])
plt.plot(x1_new,x2_new_boundary)
plt.title('Exam1 VS Exam2')
plt.xlabel('Exam1')
plt.ylabel('Exam2')
plt.legend((passed,failed),('passed','failed'))
plt.show()

如果想要进行本例子实战的数据链接如下：https://pan.baidu.com/s/1dPKCOMse7Ai1WkrJs64xBw
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