Logistic Regression

Predicted value is categorical

Classification types

  • Binary Classification
  • Multiclass Classification

Binary Classification

import pandas as pd
from matplotlib import pyplot as plt
from pathlib import Path
import numpy as np
path = Path('Data/insurance_data.csv')
df = pd.read_csv(path)
df.head()
age bought_insurance
0 22 0
1 25 0
2 47 1
3 52 0
4 46 1

\(\text{sigmoid}(z) = \dfrac{1}{1+e^-z}\) where e = Euler’s number ~ 2.71828

plt.scatter(df.age,df.bought_insurance,marker='+',color='red')

from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression
X_train, X_test, y_train, y_test = train_test_split(df[['age']],df.bought_insurance,train_size=0.8)
X_test
age
12 27
25 54
7 60
2 47
10 18
9 61 
model = LogisticRegression()
model.fit(X_train, y_train)
LogisticRegression()
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X_test
age
12 27
25 54
7 60
2 47
10 18
9 61 
y_predicted = model.predict(X_test)
y_predicted
array([0, 1, 1, 1, 0, 1])
y_probability = model.predict_proba(X_test)
model.score(X_test,y_test)
1.0
array1 = np.array(X_test)

# Stack the arrays horizontally
combined_array = np.hstack((array1, y_probability[:,1].reshape(-1, 1)))

print("Combined Array:")
print(combined_array)
Combined Array:
[[27.          0.18888707]
 [54.          0.84143616]
 [60.          0.91401439]
 [47.          0.70233749]
 [18.          0.07590529]
 [61.          0.92268871]]
sorted_array = np.sort(combined_array, 0)
sorted_array[:,0]
array([18., 27., 47., 54., 60., 61.])
plt.scatter(df.age,df.bought_insurance,marker='+',color='blue')
plt.scatter(X_test,y_test,marker='+',color='red')
plt.plot(sorted_array[:,0],sorted_array[:,1],marker='+',color='green')
plt.scatter(X_test,y_predicted,marker='*',color='green')

Multiclass Regression

from sklearn.datasets import load_digits
import matplotlib.pyplot as plt
digits = load_digits()
plt.gray() 
for i in range(2):
    plt.matshow(digits.images[i])
<Figure size 640x480 with 0 Axes>

dir(digits)
['DESCR', 'data', 'feature_names', 'frame', 'images', 'target', 'target_names']
digits.target[:]
array([0, 1, 2, ..., 8, 9, 8])
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
model = LogisticRegression()
X_train, X_test, y_train, y_test = train_test_split(digits.data,digits.target, test_size=0.2)
model.fit(X_train, y_train)
/home/ben/mambaforge/envs/cfast/lib/python3.11/site-packages/sklearn/linear_model/_logistic.py:460: ConvergenceWarning: lbfgs failed to converge (status=1):
STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.

Increase the number of iterations (max_iter) or scale the data as shown in:
    https://scikit-learn.org/stable/modules/preprocessing.html
Please also refer to the documentation for alternative solver options:
    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
  n_iter_i = _check_optimize_result(
LogisticRegression()
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model.score(X_test, y_test)
0.9722222222222222
model.predict(digits.data[0:5])
array([0, 1, 2, 3, 4])
y_predicted = model.predict(X_test)
array([5, 4, 0, 2, 9, 5, 3, 2, 0, 4, 1, 3, 5, 1, 5, 3, 6, 3, 5, 2, 3, 2,
       0, 8, 1, 9, 6, 7, 0, 8, 9, 4, 5, 7, 2, 4, 4, 4, 8, 3, 7, 8, 3, 6,
       4, 9, 2, 4, 6, 3, 5, 1, 6, 0, 7, 9, 4, 8, 8, 3, 8, 9, 5, 6, 4, 9,
       8, 5, 2, 0, 7, 7, 6, 2, 5, 8, 9, 5, 7, 5, 5, 4, 4, 8, 9, 8, 9, 2,
       1, 0, 7, 4, 8, 6, 3, 3, 3, 8, 1, 1, 5, 6, 7, 6, 1, 7, 2, 8, 1, 5,
       3, 4, 4, 9, 5, 0, 7, 0, 6, 3, 2, 2, 4, 3, 4, 8, 6, 0, 8, 0, 3, 1,
       4, 9, 0, 3, 2, 9, 9, 6, 7, 8, 4, 6, 8, 6, 9, 0, 4, 9, 7, 6, 8, 3,
       9, 6, 0, 7, 1, 7, 2, 5, 2, 3, 3, 8, 0, 0, 9, 4, 4, 5, 9, 0, 8, 8,
       7, 9, 9, 8, 3, 3, 8, 7, 0, 4, 6, 6, 1, 1, 9, 0, 3, 1, 3, 9, 2, 8,
       3, 7, 4, 5, 5, 7, 2, 1, 9, 5, 5, 7, 9, 1, 9, 1, 7, 6, 5, 1, 6, 7,
       5, 6, 7, 2, 9, 4, 9, 0, 8, 3, 3, 6, 0, 1, 3, 3, 9, 6, 1, 5, 1, 6,
       6, 3, 1, 0, 1, 0, 2, 2, 1, 9, 7, 9, 1, 0, 9, 1, 3, 8, 1, 5, 0, 0,
       8, 6, 1, 2, 6, 6, 9, 5, 3, 6, 3, 8, 9, 8, 6, 9, 7, 2, 8, 5, 9, 6,
       9, 7, 3, 7, 4, 3, 2, 1, 5, 8, 0, 8, 6, 6, 7, 5, 6, 6, 4, 6, 3, 7,
       2, 3, 6, 8, 5, 3, 1, 6, 8, 8, 9, 0, 8, 5, 6, 8, 0, 1, 2, 0, 0, 1,
       9, 6, 7, 6, 3, 2, 0, 5, 5, 2, 7, 1, 6, 4, 6, 0, 2, 5, 2, 0, 7, 6,
       9, 6, 1, 9, 1, 1, 0, 0])
from sklearn.metrics import confusion_matrix
import seaborn as sn
cm = confusion_matrix(y_test, y_predicted)
plt.figure(figsize = (10,7))
sn.heatmap(cm, annot=True)
plt.xlabel('Predicted')
plt.ylabel('Truth')
Text(95.72222222222221, 0.5, 'Truth')

from sklearn.metrics import classification_report
report = classification_report(y_test, y_predicted)
print(report)
              precision    recall  f1-score   support

           0       0.97      1.00      0.99        35
           1       0.97      0.97      0.97        36
           2       0.93      0.96      0.95        28
           3       0.97      0.95      0.96        40
           4       0.96      1.00      0.98        27
           5       0.94      0.94      0.94        35
           6       1.00      1.00      1.00        46
           7       1.00      0.97      0.98        33
           8       0.97      0.97      0.97        38
           9       0.98      0.95      0.96        42

    accuracy                           0.97       360
   macro avg       0.97      0.97      0.97       360
weighted avg       0.97      0.97      0.97       360
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