Mathematical Foundations of Machine Learning

This course provides a proof-driven introduction to the mathematical foundations of machine learning, emphasizing when and why learning is possible. The course develops learning-theoretic tools—empirical risk minimization, PAC generalization guarantees, VC dimension, and uniform convergence—and connects them to canonical models and algorithms such as linear regression, kernel methods, and neural networks as well as optimization methods including stochastic gradient descent. Students synthesize the theory through a final project: reading a research paper on theoretical machine learning or closely related area, and delivering a paired presentation, alongside an individual written report.