Mathematical Foundations and Applications

This graduate-level course will aim to cover various mathematical aspects of big and high-dimensional learning arising in data science and machine learning applications. The focus will be on building a principled understanding of randomized and relaxations methods via a mixture of empirical evaluations and mathematical modeling. Specifically, we will explore large-scale optimization algorithms for both convex and non-convex optimization, dimension reduction and random projection methods, large-scale numerical linear algebra, sparse recovery and compressed sensing, low-rank matrix recovery, convex geometry and linear inverse problems, empirical processes and generalization bounds, as well as theory and optimization landscape of deep neural networks, etc.