FRG Biweekly Meeting: Caroline Moosmueller, UNC Math

Title: Efficient learning algorithms in the Wasserstein space

Abstract: Detecting differences and building classifiers between distributions, given only finite samples, are important tasks in a number of scientific fields. Optimal transport and the Wasserstein distance have evolved as the most natural concept to deal with such tasks, but have some computational drawbacks. In this talk, I’ll describe an approximation framework through local linearizations that significantly reduces both the computational effort and the required training data in supervised learning settings. I’ll also introduce “LOT Wassmap”, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. The talk will close with some remarks on sliced optimal transport, which is a method to approximate high-dimensional transports by projected 1D transports. The proposed algorithms are demonstrated in pattern recognition tasks in imaging and medical applications.

This is joint work with Alex Cloninger, Keaton Hamm, Harish Kannan, Varun Khurana, Shiying Li, and Jinjie Zhang.

Hanes Hall 115 or https://unc.zoom.us/j/96148145615