Department of Mathematical Sciences
Cameron Musco, UMass-Amherst
Monday, February 23rd, 2026
11:00AM-11:50AM
Stratton Hall 202
Speaker: Cameron Musco, UMass-Amherst
Title: Near-optimal hierarchical matrix approximation from matrix-vector products
Abstract: In this talk, I will start by giving an overview of recent progress on the problem of structured matrix recovery from matrix-vector products. Given a target matrix A that can only be accessed through a limited number of matrix-vector products, we seek to find a near-optimal approximation to A from some structured matrix class – e.g., a low-rank approximation, a hierarchical low-rank approximation, a sparse or diagonal approximation, etc. This general problem arises across the computational sciences and data science, both in algorithmic applications and, more recently, in scientific machine learning, where it abstracts the problem of operator learning.
I will then highlight recent work in which we give the first robust approximation algorithms with relative error bounds for the important problem of recovering hierarchical low-rank (HODLR) matrices from matrix-vector products. Our results are achieved using variants of the well-studied `peeling' method for hierarchical matrix approximation, and help significantly extend existing understanding of the robustness of this approach.
Joint work with Noah Amsel (NYU), Tyler Chen (NYU -> JP Morgan), Feyza Duman Keles (NYU), Diana Halikias (Cornell -> NYU), Christopher Musco (NYU), David Persson (EPFL -> NYU)