📊 Logistic Regression

Master classification algorithms, probability theory, and the sigmoid function for binary and multiclass predictions

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Logistic Regression Curriculum

10
Core Units
~60
Key Concepts
15+
Algorithms
25+
Practical Examples
1

Introduction to Classification

Understand classification problems and how they differ from regression.

  • What is classification
  • Binary vs multiclass problems
  • Decision boundaries
  • Classification vs regression
  • Real-world applications
  • Evaluation metrics overview
  • Linear classifiers
  • Probabilistic interpretation
2

From Linear to Logistic

Transition from linear regression to logistic regression for classification.

  • Limitations of linear regression
  • Need for bounded predictions
  • Probability as output
  • Linear decision boundary
  • Link functions concept
  • Logit transformation
  • Generalized linear models
  • Mathematical motivation
3

The Sigmoid Function

Master the sigmoid function and its properties for probability modeling.

  • Sigmoid function definition
  • S-curve characteristics
  • Domain and range
  • Derivative properties
  • Odds and log-odds
  • Inverse sigmoid (logit)
  • Numerical stability
  • Alternative functions
4

Maximum Likelihood Estimation

Learn how logistic regression parameters are estimated using MLE.

  • Likelihood function
  • Log-likelihood
  • Maximum likelihood principle
  • Bernoulli distribution
  • Parameter estimation
  • Numerical optimization
  • Newton-Raphson method
  • Convergence criteria
5

Cost Function and Optimization

Understand the logistic loss function and optimization techniques.

  • Cross-entropy loss
  • Logistic loss function
  • Convex optimization
  • Gradient descent
  • Stochastic gradient descent
  • Learning rate selection
  • Convergence analysis
  • Optimization algorithms
6

Binary Classification

Implement and understand binary logistic regression in detail.

  • Binary classification setup
  • Decision threshold
  • Predicted probabilities
  • Class prediction
  • Feature importance
  • Coefficient interpretation
  • Confidence intervals
  • Model assumptions
7

Multiclass Classification

Extend logistic regression to handle multiple classes.

  • One-vs-Rest strategy
  • One-vs-One approach
  • Multinomial logistic regression
  • Softmax function
  • Cross-entropy for multiclass
  • Parameter estimation
  • Computational complexity
  • Class imbalance handling
8

Regularization Techniques

Prevent overfitting using L1 and L2 regularization methods.

  • Overfitting in logistic regression
  • Ridge regression (L2)
  • Lasso regression (L1)
  • Elastic Net regularization
  • Regularization parameter tuning
  • Feature selection with L1
  • Cross-validation
  • Bias-variance tradeoff
9

Model Evaluation

Assess logistic regression performance using appropriate metrics.

  • Confusion matrix
  • Accuracy, precision, recall
  • F1-score and F-beta
  • ROC curves and AUC
  • Precision-recall curves
  • Classification reports
  • Cross-validation strategies
  • Statistical significance tests
10

Implementation and Practice

Build logistic regression models from scratch and with libraries.

  • NumPy implementation
  • Scikit-learn usage
  • Feature preprocessing
  • Hyperparameter tuning
  • Model interpretation
  • Real-world case studies
  • Deployment considerations
  • Best practices

Unit 1: Introduction to Classification

Understand classification problems and how they differ from regression.

What is Classification

Learn the fundamental concept of classification in machine learning and supervised learning.

Supervised Learning Categorical Output Discrete Labels
Classification is a supervised learning task where the goal is to predict the category or class of new observations based on a training dataset of observations whose category membership is known.

Binary vs Multiclass Problems

Understand the difference between binary and multiclass classification problems.

Binary Classification: 2 classes (Yes/No, Spam/Not Spam, Fraud/Not Fraud)
Multiclass Classification: 3+ classes (Red/Green/Blue, Cat/Dog/Bird)
Multilabel Classification: Multiple labels per instance
# Examples of classification problems
classification_types = {
  "Binary": {
    "Email": ["Spam", "Not Spam"],
    "Medical": ["Disease", "Healthy"],
    "Finance": ["Fraud", "Legitimate"]
  },
  "Multiclass": {
    "Image": ["Cat", "Dog", "Bird", "Fish"],
    "Text": ["Sports", "Politics", "Technology"],
    "Iris": ["Setosa", "Versicolor", "Virginica"]
  }
}

Decision Boundaries

Understand how classifiers create decision boundaries to separate different classes.

Decision Boundary: The hyperplane that separates different classes in the feature space. For logistic regression, this boundary is linear and defined by the equation where the predicted probability equals 0.5.
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LogisticRegression

# Create sample 2D data
np.random.seed(42)
X = np.random.randn(100, 2)
y = (X[:, 0] + X[:, 1] > 0).astype(int)

# Fit logistic regression
model = LogisticRegression()
model.fit(X, y)

# Decision boundary: w0*x1 + w1*x2 + b = 0
w = model.coef_[0]
b = model.intercept_[0]

# Plot decision boundary
x_boundary = np.linspace(-3, 3, 100)
y_boundary = -(w[0] * x_boundary + b) / w[1]

plt.scatter(X[:, 0], X[:, 1], c=y, cmap='RdYlBu')
plt.plot(x_boundary, y_boundary, 'k-', linewidth=2)
plt.title('Logistic Regression Decision Boundary')
plt.show()

Classification vs Regression

Learn the key differences between classification and regression tasks.

Discrete Continuous Categorical Numerical
# Key differences
differences = {
  "Output Type": {
    "Classification": "Discrete/Categorical",
    "Regression": "Continuous/Numerical"
  },
  "Examples": {
    "Classification": "Email spam detection",
    "Regression": "House price prediction"
  },
  "Evaluation": {
    "Classification": "Accuracy, Precision, Recall",
    "Regression": "MSE, RMSE, MAE, R²"
  },
  "Algorithms": {
    "Classification": "Logistic Regression, SVM, Random Forest",
    "Regression": "Linear Regression, Ridge, Lasso"
  }
}

Real-world Applications

Explore practical applications of classification in various industries.

Healthcare Finance Marketing Technology
# Real-world classification applications
applications = {
  "Healthcare": [
    "Disease diagnosis from symptoms",
    "Medical image classification",
    "Drug response prediction"
  ],
  "Finance": [
    "Credit approval decisions",
    "Fraud detection systems",
    "Risk assessment models"
  ],
  "Marketing": [
    "Customer segmentation",
    "Churn prediction",
    "Ad targeting optimization"
  ],
  "Technology": [
    "Email spam filtering",
    "Image recognition",
    "Natural language processing"
  ]
}

Probabilistic Interpretation

Understand how classification can be viewed through a probabilistic lens.

Instead of hard predictions, we estimate P(y=1|X) - the probability that an instance belongs to class 1 given its features X. This probabilistic approach provides uncertainty estimates and enables better decision-making.
from sklearn.linear_model import LogisticRegression
import numpy as np

# Sample data
X = np.array([[1, 2], [2, 3], [3, 1], [4, 5]])
y = np.array([0, 0, 1, 1])

# Fit logistic regression
model = LogisticRegression()
model.fit(X, y)

# Get probability predictions
probabilities = model.predict_proba(X)
print("Probabilities for each class:")
print(probabilities)

# Get class predictions (threshold = 0.5)
predictions = model.predict(X)
print("Class predictions:", predictions)

# Custom threshold
custom_predictions = (probabilities[:, 1] > 0.3).astype(int)
print("Custom threshold predictions:", custom_predictions)