Group Invariant Dictionary Learning
Themes from numerical tensor calculus
Low-rank tensor methods compress high-dimensional arrays into more manageable sizes. This circumvents the curse of dimensionality where storage and computational costs scale exponentially with the data dimension. Over the past decade, this has enabled advances in signal processing, numerical linear algebra, machine learning, and many other fields.
Neural reconstruction of protein structure from cryo-EM images
Computing with subspaces generated by differential operators
Solving Laplace and Helmholtz problems with corner singularities via rational functions and their analogs
Spectral barriers in random certification problems
Robust Group Synchronization via Cycle-Edge Message Passing
We propose a general framework for group synchronization with adversarial corruption and sufficiently small noise. Specifically, we apply a novel message passing procedure that uses cycle consistency information in order to estimate the corruption levels of group ratios and consequently infers the corrupted group ratios and solves the synchronization problem.