Foundations of Algorithmic and Theoretical Machine Learning

Many practitioners can train machine learning models, but understanding the underlying mathematical guarantees and algorithmic design is what separates true experts from the crowd. This course bridges the gap between applying algorithms and understanding exactly why, how, and when they work. You will transition from simply writing code to analyzing model behavior, convergence rates, and generalization bounds with confidence. What you'll learn: - Understand the foundational mathematics of machine learning, including linear algebra, probability, and multivariate calculus. - Analyze empirical risk minimization and the core principles of statistical learning theory. - Evaluate generalization bounds, VC dimension, and Rademacher complexity to predict model performance on unseen data. - Apply optimization techniques, including gradient descent, stochastic gradient descent, and convex optimization formulations. - Explore algorithmic fairness, differential privacy, and robust learning paradigms in modern AI systems. - Practice translating theoretical concepts into structured algorithmic pseudocode through comprehensive written exercises. This course begins with essential mathematical terminology and foundational concepts before advancing to core learning theories and modern optimization techniques. Designed for beginners in theoretical machine learning, it requires only a basic familiarity with algebra and introductory programming. Start your journey into the mathematical heart of machine learning today.