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math.MG2024
Embedding-Projection Correspondences for the estimation of the Gromov-Hausdorff distance
Facundo Mémoli, Zane T. Smith
This writeup describes ongoing work on designing and testing a certain family of correspondences between compact metric spaces that we call \emph{embedding-projection correspondenc…
math.AT2024
Geometric Bounds for Persistence
Alexey Balitskiy, Baris Coskunuzer, Facundo Mémoli
In this paper, we offer a new perspective on persistent homology by integrating key concepts from metric geometry. For a given compact subset of a Banach space $\math…
cs.LG2024
Geometry and Stability of Supervised Learning Problems
Facundo Mémoli, Brantley Vose, Robert C. Williamson
We introduce a notion of distance between supervised learning problems, which we call the Risk distance. This distance, inspired by optimal transport, facilitates stability results…