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AI 501 Mathematics for Artificial Intelligence
Fall 2024
Course Overview
This course offers an in-depth exploration of the mathematical principles that form the foundations of machine learning (ML) and artificial intelligence (AI). Aimed at graduate students and industry professionals, this course is designed to provide a rigorous understanding of the mathematical concepts crucial for developing, implementing, and evaluating ML and AI algorithms.
In broad brush terms, we will be covering the following topics in the course:
Vector and Matrix Operations: Understanding vectors, matrices, and their operations is fundamental to data representation and transformations in ML. The course covers vector spaces, linear transformations, eigenvalues, and eigenvectors, focusing on their practical applications in data analysis and feature extraction.
Linear and Logistic Regression: Students will explore regression techniques, crucial for prediction and classification tasks. The course delves into the least squares method, regularization techniques, and logistic regression, linking theoretical concepts to practical applications in supervised learning.
Matrix Decompositions: The course includes detailed discussions on eigenvalue decomposition (EVD) and singular value decomposition (SVD), highlighting their importance in dimensionality reduction, data compression, and noise reduction.
Dimensionality Reduction: Techniques such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) are explored, providing tools to manage and visualize high-dimensional data.
Optimization Techniques: Essential for training ML models, optimization topics cover gradient descent, convex optimization, and advanced methods like Newton's method. Students will learn to implement these techniques to minimize cost functions effectively.
Probability and Statistics: Fundamental probabilistic concepts are covered, including random variables, distributions, Bayes’ theorem, and inference methods. This foundation is crucial for understanding probabilistic models and Bayesian inference.
Machine Learning Algorithms: The course includes a comprehensive overview of key ML algorithms, including Support Vector Machines (SVM), decision trees, and neural networks. Advanced topics such as deep learning and convolutional neural networks are also introduced.
Real-World Applications and Case Studies: Throughout the course, theoretical concepts are linked with practical applications through case studies and real-world examples, providing students with insights into how ML and AI are applied across various domains.
Announcements
Administrative Details
Grading Distribution
Homeworks
Quizzes
Schedule
Week 01 (Notes 01)
Week 02 (Notes 02)
Operations on vectors: Norm, Distance, Angle
Linear Independence, Span, Basis, Vector spaces, Orthonormal vectors
Week 03 (Notes 03)
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