The Department of Applied Mathematics weekly seminar is given by scholars and researchers working in applied mathematics, broadly interpreted.
Title: Bilipschitz embeddings for invariant machine learning
Abstract: Machine learning algorithms are typically designed for Euclidean data, but many natural datasets come with symmetries: a group G of isometries acts on a Euclidean space V, and points in the same orbit represent the same object. That means the true data space is not V, but the orbit space V/G. Invariant machine learning represents this quotient by a G-invariant feature map into Euclidean space. For robustness, especially against adversarial examples, this feature map should be bilipschitz with respect to the quotient metric. Sadly, vanilla polynomial invariants fail to be bilipschitz, so we need to move beyond classical invariant theory. In this talk, we present low-distortion embeddings in a variety of settings, and we conclude with several open problems.
Bio: Dustin G. Mixon is an associate professor in the Department of Mathematics at The Ohio State University. He received his PhD in Applied and Computational Mathematics from Princeton University in 2012 under the supervision of Robert Calderbank. Before joining Ohio State in 2017, he was an assistant professor at the Air Force Institute of Technology. His research interests include applied harmonic analysis, discrete geometry, and mathematical data science. Much of his work develops mathematical tools for data representations and signal reconstruction, with motivation from machine learning and signal processing.