Modern data are high-dimensional, multi-modal, and large-scale, for example, images with millions of pixels, text corpora with millions of words, gene sequences with billions of base pairs, etc. However, these data tend to concentrate on lower-dimensional, nonlinear subspaces known as manifolds. Learning and sampling from this real distribution, hence, is of tremendous value. This class covers the mathematical theory of high-dimensional geometry and manifolds and how it applies to the latest advances in artificial intelligence.
- Time: Mon/Wed 2:00 - 3:15 PM
- Location: Thornton E304 / Zoom
- Instructor: Tom Fletcher (ptf8v AT virginia DOT edu)
- Office Hours: Tuesdays 11 AM - 12 noon, Rice 306
- TA: Nian (Nellie) Wu (bsw3ac AT virginia DOT edu)
- Office Hours: Thursdays 5 - 6 PM, Rice 303
- Prerequisites: You should have basic (undergraduate level) knowledge of Probability, Linear Algebra, Multivariate Calculus, and be comfortable programming in Python
- Software: All homeworks will be done in Jupyter
Manfredo do Carmo, Riemannian Geometry
Sigmundur Gudmundsson, Introduction to Riemannian Geometry
For those of you who are relatively new to Jupyter, here are a few notebooks that you might find useful (from my undergraduate course Foundations of Data Analysis.)