Machine Learning: Algorithms and Applications¶

Title: Machine Learning: Algorithms and Applications

Target Audience: College undergraduate

Prerequisites: Linear algebra, calculus, and some Python programming experience

Course Overview¶

This comprehensive textbook provides a rigorous yet accessible introduction to machine learning, covering the fundamental algorithms that power modern artificial intelligence systems. Designed for students with a background in linear algebra, calculus, and programming, this course explores both the theoretical foundations and practical implementations of essential machine learning methods.

The text begins with supervised learning, starting with the intuitive k-nearest neighbors algorithm to establish core concepts of classification and regression. Students then progress to decision trees, learning how these interpretable models partition feature space and handle both categorical and continuous data. The course covers logistic regression for binary and multiclass classification, emphasizing probabilistic interpretations and optimization techniques. Support vector machines are explored in depth, including the kernel trick and margin maximization principles that make SVMs powerful for complex classification tasks.

The unsupervised learning section focuses on k-means clustering, teaching students how to discover natural groupings in unlabeled data, understand convergence properties, and select appropriate numbers of clusters. Practical considerations such as initialization strategies and distance metrics are thoroughly examined.

Neural networks form the culminating section of the course. Students begin with fully connected neural networks, learning about activation functions, backpropagation, and gradient descent optimization. The text then advances to convolutional neural networks (CNNs), explaining how these architectures exploit spatial structure for computer vision tasks through convolution operations, pooling layers, and hierarchical feature learning. The course concludes with transfer learning, demonstrating how pre-trained models can be adapted to new tasks with limited data, a crucial technique for real-world applications.

Each chapter includes mathematical derivations, algorithmic pseudocode, implementation exercises in Python using popular libraries (scikit-learn, TensorFlow/PyTorch), and real-world case studies. Students will develop both theoretical understanding and practical machine learning engineering skills, preparing them for advanced coursework or industry applications in data science and artificial intelligence.

Main Topics Covered¶

• K-nearest neighbors (KNN) algorithm
• Decision trees for classification and regression
• Logistic regression for binary and multiclass classification
• Support vector machines (SVMs) and kernel methods
• K-means clustering
• Fully connected neural networks
• Convolutional neural networks (CNNs)
• Transfer learning

Topics Not Covered¶

This course does not cover: - Reinforcement learning - Recurrent neural networks (RNNs) and LSTMs - Generative adversarial networks (GANs) - Natural language processing specific techniques - Advanced optimization methods beyond gradient descent - Bayesian methods and probabilistic graphical models - Ensemble methods (Random Forests, Gradient Boosting, XGBoost) - Dimensionality reduction techniques (PCA, t-SNE) - Time series analysis - Advanced deep learning architectures (Transformers, Attention mechanisms)

Learning Outcomes¶

After completing this course, students will be able to:

Remember¶

Retrieving, recognizing, and recalling relevant knowledge from long-term memory.

• Recall the key hyperparameters for each machine learning algorithm (k in KNN, learning rate, regularization parameters, etc.)
• Recognize the mathematical notation used in machine learning (vectors, matrices, loss functions, gradients)
• List the steps in the backpropagation algorithm
• Identify common activation functions (sigmoid, tanh, ReLU, softmax) and their properties
• Recall the differences between supervised and unsupervised learning
• Remember the convergence criteria for k-means clustering
• List the components of a convolutional neural network (convolution layers, pooling layers, fully connected layers)

Understand¶

Constructing meaning from instructional messages, including oral, written, and graphic communication.

• Explain how the k-nearest neighbors algorithm makes predictions for classification and regression
• Describe the decision boundary created by different machine learning algorithms
• Interpret the role of the kernel trick in support vector machines
• Explain the concept of margin maximization in SVMs
• Clarify the difference between parametric and non-parametric models
• Summarize how gradient descent optimizes loss functions
• Explain the vanishing gradient problem and how ReLU addresses it
• Describe how convolution operations preserve spatial structure in images
• Interpret confusion matrices, ROC curves, and other evaluation metrics
• Explain the bias-variance tradeoff

Apply¶

Carrying out or using a procedure in a given situation.

• Implement k-nearest neighbors from scratch in Python
• Apply decision tree algorithms using scikit-learn
• Use logistic regression for binary and multiclass classification problems
• Train support vector machines with different kernel functions
• Execute k-means clustering on unlabeled datasets
• Build and train fully connected neural networks using TensorFlow/PyTorch
• Construct convolutional neural networks for image classification tasks
• Apply transfer learning to adapt pre-trained models to new datasets
• Select appropriate evaluation metrics for different problem types
• Tune hyperparameters using cross-validation
• Preprocess data (normalization, standardization, one-hot encoding)

Analyze¶

Breaking material into constituent parts and determining how the parts relate to one another and to an overall structure or purpose.

• Compare the performance of different algorithms on the same dataset
• Analyze learning curves to diagnose overfitting and underfitting
• Determine which algorithm is most appropriate for a given problem based on data characteristics
• Examine the impact of different hyperparameters on model performance
• Break down the computational complexity of various algorithms
• Investigate feature importance in decision trees
• Analyze the effect of different kernel functions on SVM decision boundaries
• Examine the hierarchical features learned by different layers in CNNs
• Distinguish between cases where transfer learning will be effective versus ineffective

Evaluate¶

Making judgments based on criteria and standards through checking and critiquing.

• Assess model performance using appropriate metrics (accuracy, precision, recall, F1-score, AUC)
• Critique the choice of algorithm for a specific real-world application
• Judge the quality of data preprocessing steps
• Evaluate whether a model is overfitting or underfitting based on training and validation curves
• Assess the interpretability versus performance tradeoff for different models
• Critique experimental design in machine learning research papers
• Evaluate the ethical implications of deploying machine learning models in sensitive domains
• Judge when more data versus better features will improve model performance

Create¶

Putting elements together to form a coherent or functional whole; reorganizing elements into a new pattern or structure.

• Design a complete machine learning pipeline from data collection to deployment
• Develop custom neural network architectures for novel problems
• Create ensemble methods by combining multiple algorithms
• Design experiments to compare different approaches to a machine learning problem
• Synthesize knowledge from multiple algorithms to solve complex real-world problems
• Build an end-to-end image classification system using CNNs
• Construct a machine learning solution for a business problem, including problem formulation, data analysis, model selection, and evaluation
• Design and implement a capstone project that applies multiple machine learning techniques to a domain-specific problem (e.g., medical diagnosis, fraud detection, recommendation systems, autonomous systems)
• Create visualizations to communicate model insights to non-technical stakeholders