Here are 100 chapter titles for a book on Machine Learning Algorithms, progressing from beginner to advanced, with a focus on the underlying mathematics:
I. Foundations (1-20)
- Introduction to Machine Learning: What and Why?
- Types of Machine Learning: Supervised, Unsupervised, Reinforcement
- Data Representation: Features, Labels, and Datasets
- Mathematical Foundations: Linear Algebra Review
- Mathematical Foundations: Calculus Review
- Mathematical Foundations: Probability and Statistics Review
- Model Evaluation Metrics: Accuracy, Precision, Recall, F1-Score
- Bias-Variance Tradeoff: Understanding Generalization
- Overfitting and Underfitting: Diagnosing Model Performance
- Regularization: L1 and L2 Regularization Techniques
- Feature Engineering: Creating Effective Features
- Data Preprocessing: Cleaning and Transforming Data
- Dimensionality Reduction: PCA and Feature Selection
- Model Selection: Choosing the Best Model
- Hyperparameter Tuning: Optimizing Model Parameters
- Introduction to Optimization: Gradient Descent
- Linear Algebra for Machine Learning: Vectors and Matrices
- Calculus for Machine Learning: Derivatives and Gradients
- Probability for Machine Learning: Distributions and Bayes' Theorem
- Review and Preview: Looking Ahead
II. Supervised Learning (21-50)
- Linear Regression: Predicting Continuous Values
- Linear Regression: Mathematical Formulation
- Linear Regression: Gradient Descent Implementation
- Polynomial Regression: Fitting Non-Linear Relationships
- Logistic Regression: Predicting Categorical Values
- Logistic Regression: The Sigmoid Function and Decision Boundaries
- Logistic Regression: Maximum Likelihood Estimation
- Support Vector Machines (SVM): Finding Optimal Hyperplanes
- SVM: The Kernel Trick for Non-Linear Separability
- SVM: Mathematical Formulation and Optimization
- Decision Trees: Building Tree-Based Classifiers
- Decision Trees: Entropy and Information Gain
- Decision Trees: Pruning to Avoid Overfitting
- Random Forests: Ensemble Learning with Decision Trees
- Random Forests: Bagging and Feature Randomization
- Naive Bayes: Probabilistic Classification
- Naive Bayes: Bayes' Theorem and Feature Independence
- K-Nearest Neighbors (KNN): Instance-Based Learning
- KNN: Distance Metrics and Choosing K
- Linear Discriminant Analysis (LDA): Finding Optimal Projections
- Quadratic Discriminant Analysis (QDA): Relaxing Linearity Assumptions
- Perceptron: A Simple Linear Classifier
- Multilayer Perceptron (MLP): Neural Networks
- Backpropagation: Training Neural Networks
- Activation Functions: Sigmoid, ReLU, and Others
- Neural Network Architectures: Deep Learning Basics
- Convolutional Neural Networks (CNNs): Image Recognition
- Recurrent Neural Networks (RNNs): Sequence Data
- Long Short-Term Memory (LSTM) Networks: Handling Long-Range Dependencies
- Review and Practice: Supervised Learning
III. Unsupervised Learning (51-70)
- Clustering: Grouping Similar Data Points
- K-Means Clustering: Partitioning Data into Clusters
- K-Means Clustering: The Elbow Method and Choosing K
- Hierarchical Clustering: Building a Hierarchy of Clusters
- Agglomerative Clustering: Bottom-Up Approach
- Divisive Clustering: Top-Down Approach
- DBSCAN: Density-Based Clustering
- Gaussian Mixture Models (GMMs): Probabilistic Clustering
- Expectation-Maximization (EM) Algorithm: Fitting GMMs
- Principal Component Analysis (PCA): Dimensionality Reduction
- PCA: Mathematical Formulation and Eigenvalue Decomposition
- Independent Component Analysis (ICA): Separating Independent Signals
- t-SNE: Visualizing High-Dimensional Data
- Autoencoders: Learning Compressed Representations
- Generative Adversarial Networks (GANs): Generating Data
- GANs: Training GANs and Challenges
- Variational Autoencoders (VAEs): Probabilistic Autoencoders
- Self-Organizing Maps (SOMs): Neural Network-Based Clustering
- Association Rule Mining: Finding Relationships in Data
- Review and Practice: Unsupervised Learning
IV. Reinforcement Learning (71-80)
- Introduction to Reinforcement Learning: Agents and Environments
- Markov Decision Processes (MDPs): Formalizing RL Problems
- Bellman Equations: Optimality in RL
- Dynamic Programming: Solving MDPs
- Monte Carlo Methods: Learning from Episodes
- Temporal Difference Learning: Combining DP and MC
- Q-Learning: Learning Action Values
- SARSA: On-Policy Learning
- Deep Reinforcement Learning: Combining RL with Deep Learning
- Review and Practice: Reinforcement Learning
V. Advanced Topics and Applications (81-100)
- Bayesian Learning: Updating Beliefs with Data
- Gaussian Processes: Non-parametric Regression
- Ensemble Methods: Boosting and Stacking
- Gradient Boosting Machines: XGBoost, LightGBM, CatBoost
- Model Interpretability: Understanding Model Decisions
- Explainable AI (XAI): Techniques for Explaining AI Models
- Fairness in Machine Learning: Addressing Bias
- Adversarial Machine Learning: Defending Against Attacks
- Transfer Learning: Leveraging Pre-trained Models
- Deep Learning Architectures: ResNet, Inception, Transformer
- Natural Language Processing (NLP): Text Analysis and Understanding
- Computer Vision: Image Recognition and Processing
- Recommender Systems: Personalized Recommendations
- Time Series Analysis: Forecasting and Prediction
- Anomaly Detection: Identifying Unusual Patterns
- Machine Learning Pipelines: Building End-to-End Systems
- Cloud Computing for Machine Learning: Scaling ML Applications
- Ethics in Machine Learning: Responsible AI Development
- History of Machine Learning: A Detailed Account
- Open Problems and Future Directions in Machine Learning