MATH5466

This course gives an overview of the mathematical foundations for some commonly used techniques in machine learning and data science. The course will cover unsupervised learning techniques (Johnson-Lindenstrauss randomized embeddings, spectral embeddings and diffusion maps, the t-distributed stochastic neighbor embedding, low-rank approximations), neural networks and deep learning (auto-differentiation, universal approximation, graph-neural networks), advanced techniques in graph-based learning (graph-cuts and graph total variation, active learning, semi-supervised learning at low label rates), and optimization for machine learning (iteratively reweighted least squares (IRLS), momentum descent, stochastic optimization, proximal gradient descent, Newton's method, matrix optimization and matrix calculus, matrix completion, and the continuum perspective on optimization).
Prerequisites: Math 5465. Linear algebra (for example MATH 2142, 2243 or 2373) and
multivariable calculus (for example MATH 2263 or 2374), or consent of the instructor.