python 逻辑回归（初学者）

Question

我正在努力使用 python 自学一些逻辑回归。我正在尝试应用演练中的课程 here to the small dataset in the wikipedia entryhere。

好像不太对劲。 Wikipedia 和 Excel 求解器（使用 this video 中的方法验证）给出截距 -4.0777 和系数 1.5046，但我从 github 示例中构建的代码分别输出 -0.924200 和 0.756024。

我尝试使用的代码如下。有什么明显的错误吗？

import numpy as np
import pandas as pd
from patsy import dmatrices
from sklearn.linear_model import LogisticRegression


X = [0.5,0.75,1.0,1.25,1.5,1.75,1.75,2.0,2.25,2.5,2.75,3.0,3.25,
3.5,4.0,4.25,4.5,4.75,5.0,5.5]
y = [0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1]

zipped = list(zip(X,y))
df = pd.DataFrame(zipped,columns = ['study_hrs','p_or_f'])

y, X = dmatrices('p_or_f ~ study_hrs',
                  df, return_type="dataframe")

y = np.ravel(y)

model = LogisticRegression()
model = model.fit(X,y)
print(pd.DataFrame(np.transpose(model.coef_),X.columns))

>>>
                  0
Intercept -0.924200
study_hrs  0.756024

Answer 1

解决方案

只需将模型创建行更改为

model = LogisticRegression(C=100000, fit_intercept=False)

问题分析

默认情况下，sklearn求解正则化LogisticRegression，拟合强度C=1（小C-大正则化，大C-小正则化）。

This class implements regularized logistic regression using the liblinear library, newton-cg and lbfgs solvers. It can handle both dense and sparse input. Use C-ordered arrays or CSR matrices containing 64-bit floats for optimal performance; any other input format will be converted (and copied).

因此要获得他们的模型你应该适合

model = LogisticRegression(C=1000000)

这给出了

Intercept -2.038853 # this is actually half the intercept
study_hrs  1.504643 # this is correct

此外，问题还在于您在 patsy 中处理数据的方式，请参阅简化的正确示例

import numpy as np
from sklearn.linear_model import LogisticRegression

X = [0.5,0.75,1.0,1.25,1.5,1.75,1.75,2.0,2.25,2.5,2.75,3.0,3.25,
3.5,4.0,4.25,4.5,4.75,5.0,5.5]
y = [0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1]

X = np.array([[x] for x in X])
y = np.ravel(y)

model = LogisticRegression(C=1000000.)
model = model.fit(X,y)

print('coef', model.coef_)
print('intercept', model.intercept_)

给予

coef [[ 1.50464059]]
intercept [-4.07769916]

到底是什么问题？当您执行 dmatrices 时，默认情况下会将您的输入数据嵌入一列（偏差）

X = [0.5,0.75,1.0,1.25,1.5,1.75,1.75,2.0,2.25,2.5,2.75,3.0,3.25,
3.5,4.0,4.25,4.5,4.75,5.0,5.5]
y = [0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1]

zipped = list(zip(X,y))
df = pd.DataFrame(zipped,columns = ['study_hrs','p_or_f'])

y, X = dmatrices('p_or_f ~ study_hrs',
                  df, return_type="dataframe")

print(X)

这导致

    Intercept  study_hrs
0           1       0.50
1           1       0.75
2           1       1.00
3           1       1.25
4           1       1.50
5           1       1.75
6           1       1.75
7           1       2.00
8           1       2.25
9           1       2.50
10          1       2.75
11          1       3.00
12          1       3.25
13          1       3.50
14          1       4.00
15          1       4.25
16          1       4.50
17          1       4.75
18          1       5.00
19          1       5.50

这就是为什么产生的偏差只是真实偏差的一半 - scikit 学习还添加了一列 1... 所以你现在有 两个偏差，因此最佳解决方案是给每个偏差一半的权重。

那你能做什么？

不要这样使用patsy
禁止patsy添加偏见
告诉 sklearn 不要添加偏差

.

import numpy as np
import pandas as pd
from patsy import dmatrices
from sklearn.linear_model import LogisticRegression

X = [0.5,0.75,1.0,1.25,1.5,1.75,1.75,2.0,2.25,2.5,2.75,3.0,3.25,
3.5,4.0,4.25,4.5,4.75,5.0,5.5]
y = [0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1]

zipped = list(zip(X,y))
df = pd.DataFrame(zipped,columns = ['study_hrs','p_or_f'])

y, X = dmatrices('p_or_f ~ study_hrs',
                  df, return_type="dataframe")

y = np.ravel(y)

model = LogisticRegression(C=100000, fit_intercept=False)
model = model.fit(X,y)
print(pd.DataFrame(np.transpose(model.coef_),X.columns))

给予

Intercept -4.077571
study_hrs  1.504597

随心所欲

python 逻辑回归（初学者）

python logistic regression (beginner)

python

machine-learning

scikit-learn

logistic-regression

patsy

解决方案

问题分析