Melanie Weber
Assistant Professor of Applied Mathematics and of Computer Science, Harvard University
Wed, Oct 11, 2023
7:30 PM UTC
Wed, Oct 11, 2023
7:30 PM UTC
In-person
4 Thomas More St
London E1W 1YW, UK
London E1W 1YW, UK
The Roux Institute
Room
100 Fore Street
Portland, ME 04101
Portland, ME 04101
Network Science Institute
2nd floor
2nd floor
Network Science Institute
11th floor
11th floor
177 Huntington Ave
Boston, MA 02115
Boston, MA 02115
Room
58 St Katharine's Way
London E1W 1LP, UK
London E1W 1LP, UK
Talk recording
The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of Representation Learning. In this talk, we study this problem from the perspective of Discrete Geometry. We start by reviewing discrete notions of curvature with a focus on discrete Ricci curvature. Then we discuss how curvature is linked to mesoscale structure in graphs, which gives rise to applications in graph machine learning, such as (unsupervised) node clustering. For downstream machine learning and data science applications, it is often beneficial to represent graph-structured data in a continuous space, which may be Euclidean or Non-Euclidean. We show that discrete curvature allows for characterizing the geometry of a suitable embedding space both locally and in the sense of global curvature bounds and discuss implications of those results in graph machine learning.
About the speaker
Melanie is an Assistant Professor of Applied Mathematics and of Computer Science at Harvard University. Her research focuses on utilizing geometric structure in data for the design of efficient Machine Learning and Optimization methods. In 2021-2022, she was a Hooke Research Fellow at the Mathematical Institute in Oxford. Previously, she received her PhD from Princeton University (2021). She is a recipient of the 2023 IMA Leslie Fox Prize in Numerical Analysis, a Simons-Berkeley Research Fellowship and Princeton’s C.V. Starr Fellowship.
Share this page: