Large-Scale Machine Learning: Mathematical Foundations and Applications

Catalog description

This course covers 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 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 neural networks, etc. The course material builds upon the basic principles of machine learning, using multivariate calculus, linear algebra, basic probability, and algorithms. Emphasis will be on producing mathematical arguments and rigorous proofs.