Position: Hooke Research Fellow
Current Institution: University of Oxford
Abstract: Geometric Methods for Machine Learning and Optimization
A key challenge in machine learning and optimization is the identification of geometric structure in high-dimensional data. Such structural understanding is of great value for the design of efficient algorithms and for developing fundamental guarantees for their performance. I will present two lines of work that utilize Riemannian geometry in machine learning and data science. First we consider the task of learning a robust classifier in hyperbolic space. Such spaces have received a surge of interest for representing large-scale hierarchical data since they achieve better representation accuracy with fewer dimensions. Secondly we consider the problem of optimizing a function on a Riemannian manifold. Specifically we will consider classes of optimization problems where exploiting Riemannian geometry can deliver algorithms that are computationally superior to standard (Euclidean) approaches.
Melanie is a Hooke Research Fellow at the Mathematical Institute at the University of Oxford. Her research focuses on understanding the geometric features of data mathematically and on developing machine learning methods that utilize this knowledge. She received her Ph.D. from Princeton University in 2021 where she was advised by Charles Fefferman and also spent time at MITÂ’s Laboratory for Information and Decision Systems the Max Planck Institute for Mathematics in the Sciences and the research labs of Facebook Google and Microsoft. In addition to her academic work she is the Chief Scientist of the Legal AI startup Claudius Legal Intelligence. Her awards include Princeton’s C.V. Starr Fellowship (2016) a U.S. Junior Oberwolfach Fellowship (2018) as well as a Simons-Berkeley Fellowship (2021).