I have made some experiments with logistic regression in R, python statmodels and sklearn. While the results given by R and statmodels agree, there is some discrepency with what is returned by sklearn. I would like to understand why these results are different.
I understand that it is probably not the same optimization algorithms that are used under the wood.
Specifically, I use the standard Default
dataset (used in the ISL book). The following Python code reads the data into a dataframe Default
.
import pandas as pd
# data is available here
Default = pd.read_csv('https://d1pqsl2386xqi9.cloudfront.net/notebooks/Default.csv', index_col=0)
#
Default['default']=Default['default'].map({'No':0, 'Yes':1})
Default['student']=Default['student'].map({'No':0, 'Yes':1})
#
I=Default['default']==0
print("Number of 'default' values :", Default[~I]['balance'].count())
Number of 'default' values : 333.
There is a total of 10000 examples, with only 333 positives
Logistic regression in R
I use the following
library("ISLR")
data(Default,package='ISLR')
#write.csv(Default,"default.csv")
glm.out=glm('default~balance+income+student', family=binomial, data=Default)
s=summary(glm.out)
print(s)
#
glm.probs=predict(glm.out,type="response")
glm.probs[1:5]
glm.pred=ifelse(glm.probs>0.5,"Yes","No")
#attach(Default)
t=table(glm.pred,Default$default)
print(t)
score=mean(glm.pred==Default$default)
print(paste("score",score))
The result is as follows
Call: glm(formula = "default~balance+income+student", family =
binomial,
data = Default)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.4691 -0.1418 -0.0557 -0.0203 3.7383
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.087e+01 4.923e-01 -22.080 < 2e-16
balance 5.737e-03 2.319e-04 24.738 < 2e-16
income 3.033e-06 8.203e-06 0.370 0.71152
studentYes -6.468e-01 2.363e-01 -2.738 0.00619
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 2920.6 on 9999 degrees of freedom Residual
deviance: 1571.5 on 9996 degrees of freedom AIC: 1579.5
Number of Fisher Scoring iterations: 8
glm.pred No Yes
No 9627 228
Yes 40 105
1 "score 0.9732"
I am too lazy to cut and paste the results obtained with statmodels. It suffice to say that they are extremely similar to those given by R.
sklearn
For sklearn, I ran the following code.
- There is a parameter class_weight for taking into account unbalanced classes. I tested class_weight=None (no weightening -- I think that is the default in R), and class_weight='auto' (weightening with the inverse frequencies found inthe data)
- I also put C=10000,the inverse of the regularization parameter, so as to minimize the effect of regularization.
~~
import sklearn
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import confusion_matrix
features = Default[[ 'balance', 'income' ]]
target = Default['default']
#
for weight in (None, 'auto'):
print("*"*40+"
weight:",weight)
classifier = LogisticRegression(C=10000, class_weight=weight, random_state=42)
#C=10000 ~ no regularization
classifier.fit(features, target,) #fit classifier on whole base
print("Intercept", classifier.intercept_)
print("Coefficients", classifier.coef_)
y_true=target
y_pred_cls=classifier.predict_proba(features)[:,1]>0.5
C=confusion_matrix(y_true,y_pred_cls)
score=(C[0,0]+C[1,1])/(C[0,0]+C[1,1]+C[0,1]+C[1,0])
precision=(C[1,1])/(C[1,1]+C[0 ,1])
recall=(C[1,1])/(C[1,1]+C[1,0])
print("
Confusion matrix")
print(C)
print()
print('{s:{c}<{n}}{num:2.4}'.format(s='Score',n=15,c='', num=score))
print('{s:{c}<{n}}{num:2.4}'.format(s='Precision',n=15,c='', num=precision))
print('{s:{c}<{n}}{num:2.4}'.format(s='Recall',n=15,c='', num=recall))
The results are given below.
> ****************************************
>weight: None
>
>Intercept [ -1.94164126e-06]
>
>Coefficients [[ 0.00040756 -0.00012588]]
>
> Confusion matrix
>
> [[9664 3]
> [ 333 0]]
>
> Score 0.9664
> Precision 0.0
> Recall 0.0
>
> ****************************************
>weight: auto
>
>Intercept [-8.15376429]
>
>Coefficients
>[[ 5.67564834e-03 1.95253338e-05]]
>
> Confusion matrix
>
> [[8356 1311]
> [ 34 299]]
>
> Score 0.8655
> Precision 0.1857
> Recall 0.8979
What I observe is that for class_weight=None
, the Score is excellent but no positive example is recognized. Precision and recall are at zero. The coefficients found are very small, particularly the intercept. Modifying C does not change things.
For class_weight='auto'
things seems better but I still have a precision which is very low (too much positive classified).
Again, changing C does not help. If I modify the intercept by hand, I can recover the results given by R. So I suspect that here is a discrepency between the estimation of the intecepts in the two cases. As this has a consequence in the specification of the threeshold (analog to a resampling of pulations), this can explain the differences in performances.
However, I would welcome any advice for the choice between the two solutions and help to understand the origin of these differences. Thanks.
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