4 papers
Persistent Classification: A New Approach to Stability of Data and Adversarial Examples
Brian Bell, Michael Geyer, David Glickenstein +4
There are a number of hypotheses underlying the existence of adversarial examples for classification problems. These include the high-dimensionality of the data, high codimension i…
Manifold learning in Wasserstein space
Keaton Hamm, Caroline Moosmüller, Bernhard Schmitzer +1
This paper aims at building the theoretical foundations for manifold learning algorithms in the space of absolutely continuous probability measures …
Structured Approximations of Measures
Keaton Hamm, Varun Khurana
We study the approximation of probability measures in the Wasserstein- distance by structured classes of approximators, motivated by applications in imaging, machine learning, a…
On Wasserstein distances for affine transformations of random vectors
Keaton Hamm, Andrzej Korzeniowski
We expound on some known lower bounds of the quadratic Wasserstein distance between random vectors in with an emphasis on affine transformations that have been used…