4 papers
Estimating the Euclidean distortion of an orbit space
Ben Blum-Smith, Harm Derksen, Dustin G. Mixon +2
Given a finite-dimensional inner product space and a group of isometries, we consider the problem of embedding the orbit space into a Hilbert space in a way that pres…
Recovering a group from few orbits
Dustin G. Mixon, Brantley Vose
For an unknown finite group of automorphisms of a finite-dimensional Hilbert space, we find sharp bounds on the number of generic -orbits needed to recover up to group i…
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…
Harmonic Representatives in Homology over Arbitrary Fields
Michael J. Catanzaro, Brantley Vose
We introduce a notion of harmonic chain for chain complexes over fields of positive characteristic. A list of conditions for when a Hodge decomposition theorem holds in this settin…