%%html
<!-- The customized css for the slides -->
<link rel="stylesheet" type="text/css" href="../styles/python-programming-introduction.css"/>
<link rel="stylesheet" type="text/css" href="../styles/basic.css"/>
<link rel="stylesheet" type="text/css" href="../../assets/styles/basic.css" />

# Install the necessary dependencies

import os
import sys
!{sys.executable} -m pip install --quiet pandas scikit-learn numpy matplotlib jupyterlab_myst ipython

43.13. Logistic Regression#

43.13.1. Introduction#

  • In fact, logistic regression is a classification algorithm, unlike other regression models.

  • Logistic Regression is very important for entering deep learning.

  • After understanding this topic, you will be able to easily learning to Artificial Neural Network.

43.13.2. Importing the libraries#

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

43.13.3. Sigmoid function#

def sigmoid(x):
    return 1.0 / (1.0 + np.exp(-x))

values = np.arange(-10, 10, 0.1)

plt.plot(values, sigmoid(values))
plt.xlabel('x')
plt.ylabel('sigmoid(x)')
plt.title('Sigmoid Function in Matplotlib')
plt.show()

43.13.4. Importing the dataset#

dataset = pd.read_csv('../../assets/data/Social_Network_Ads.csv')
X = dataset.iloc[:, :-1].values
y = dataset.iloc[:, -1].values

dataset

43.13.5. Splitting the dataset into the Training set and Test set#

from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.25, random_state = 0)

43.13.6. Feature Scaling#

from sklearn.preprocessing import StandardScaler
sc = StandardScaler()
X_train = sc.fit_transform(X_train)
X_test = sc.transform(X_test)

43.13.7. Training the Logistic Regression model on the Training set#

from sklearn.linear_model import LogisticRegression
classifier = LogisticRegression(random_state = 0)
classifier.fit(X_train, y_train)

43.13.8. Predicting a new result#

print(classifier.predict(sc.transform([[30, 87000], [65, 990000]])))

43.13.9. Predicting the Test set results#

y_pred = classifier.predict(X_test)
print(np.concatenate((y_pred.reshape(len(y_pred),1), y_test.reshape(len(y_test),1)), 1))

43.13.10. Making the Confusion Matrix#

from sklearn.metrics import confusion_matrix, accuracy_score
cm = confusion_matrix(y_test, y_pred)
print(cm)
accuracy_score(y_test, y_pred)

43.13.11. Visualising the Training set results#

from matplotlib.colors import ListedColormap
X_set, y_set = sc.inverse_transform(X_train), y_train
X1, X2 = np.meshgrid(np.arange(start = X_set[:, 0].min() - 10, stop = X_set[:, 0].max() + 10, step = 0.5),
                     np.arange(start = X_set[:, 1].min() - 1000, stop = X_set[:, 1].max() + 1000, step = 0.5))
plt.contourf(X1, X2, classifier.predict(sc.transform(np.array([X1.ravel(), X2.ravel()]).T)).reshape(X1.shape),
             alpha = 0.75, cmap = ListedColormap(('red', 'green')))
plt.xlim(X1.min(), X1.max())
plt.ylim(X2.min(), X2.max())
for i, j in enumerate(np.unique(y_set)):
    plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1], c = ListedColormap(('red', 'green'))(i), label = j)
plt.title('Logistic Regression (Training set)')
plt.xlabel('Age')
plt.ylabel('Estimated Salary')
plt.legend()
plt.show()

43.13.12. Visualising the Test set results#

from matplotlib.colors import ListedColormap
X_set, y_set = sc.inverse_transform(X_test), y_test
X1, X2 = np.meshgrid(np.arange(start = X_set[:, 0].min() - 10, stop = X_set[:, 0].max() + 10, step = 0.5),
                     np.arange(start = X_set[:, 1].min() - 1000, stop = X_set[:, 1].max() + 1000, step = 0.5))
plt.contourf(X1, X2, classifier.predict(sc.transform(np.array([X1.ravel(), X2.ravel()]).T)).reshape(X1.shape),
             alpha = 0.75, cmap = ListedColormap(('red', 'green')))
plt.xlim(X1.min(), X1.max())
plt.ylim(X2.min(), X2.max())
for i, j in enumerate(np.unique(y_set)):
    plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1], c = ListedColormap(('red', 'green'))(i), label = j)
plt.title('Logistic Regression (Test set)')
plt.xlabel('Age')
plt.ylabel('Estimated Salary')
plt.legend()
plt.show()

43.13.13. Linear Regression v.s. Logistic Regression#

from sklearn.datasets import make_classification

X, y = make_classification(
    n_features=2, n_redundant=0, n_informative=2, n_clusters_per_class=1, random_state=12
)

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.25, random_state = 0)

plt.scatter(X[:, 0], X[:, 1], c=y)

plt.plot([-2.0, 0], [1.2, -1.3])

from sklearn.linear_model import LogisticRegression

classifier = LogisticRegression(random_state = 0)
classifier.fit(X_train, y_train)

classifier.__dict__

print(1.4/2.4)

print(1.3/2.4)

from sklearn.metrics import confusion_matrix, accuracy_score

y_pred = classifier.predict(X_test)

cm = confusion_matrix(y_test, y_pred)
print(cm)
accuracy_score(y_test, y_pred)

classifier.coef_

43.13.14. Logistic Regression from scratch#

class MyOwnLogisticRegression:
    def __init__(self, learning_rate=0.001, n_iters=1000):
        self.lr = learning_rate
        self.n_iters = n_iters
        self.weights = None
        self.bias = None

    def fit(self, X, y):
        n_samples, n_features = X.shape

        # init parameters
        self.weights = np.zeros(n_features)
        self.bias = 0

        # gradient descent
        for _ in range(self.n_iters):
            # approximate y with linear combination of weights and x, plus bias
            linear_model = np.dot(X, self.weights) + self.bias
            # apply sigmoid function
            y_predicted = self._sigmoid(linear_model)

            # compute gradients
            dw = (1 / n_samples) * np.dot(X.T, (y_predicted - y))
            db = (1 / n_samples) * np.sum(y_predicted - y)
            # update parameters
            self.weights -= self.lr * dw
            self.bias -= self.lr * db

    def predict(self, X):
        linear_model = np.dot(X, self.weights) + self.bias
        y_predicted = self._sigmoid(linear_model)
        y_predicted_cls = [1 if i > 0.5 else 0 for i in y_predicted]
        return np.array(y_predicted_cls)

    def _sigmoid(self, x):
        return 1 / (1 + np.exp(-x))

my_own_classifier = MyOwnLogisticRegression()
my_own_classifier.fit(X_train, y_train)

y_pred = my_own_classifier.predict(X_test)

cm = confusion_matrix(y_test, y_pred)
print(cm)
accuracy_score(y_test, y_pred)

43.13.15. Loss function for logistic regression#

43.13.15.1. Cross-entropy#

def loss(self, h, y):
    return (-y * np.log(h) - (1 - y) * np.log(1 - h)).mean()

43.13.16. Linear separability#

from sklearn.datasets import make_moons

X, y = make_moons(noise=0.3, random_state=0)

plt.scatter(X[:, 0], X[:, 1], c=y)

from sklearn.datasets import make_circles

X, y = make_circles(noise=0.3, factor=0.5, random_state=0)

plt.scatter(X[:, 0], X[:, 1], c=y)

43.13.16.1. That’s when Neural Network comes into play!#

43.13.17. Acknowledgments#

Thanks to ERENCAN for creating the open-source Kaggle jupyter notebook, licensed under Apache 2.0. It inspires the majority of the content of this assignment.