The 1W-MINDS Seminar was founded in the early days of the COVID-19 pandemic to mitigate the impossibility of travel. We have chosen to continue the seminar since to help form the basis of an inclusive community interested in mathematical data science, computational harmonic analysis, and related applications by providing free access to high quality talks without the need to travel. In the spirit of environmental and social sustainability, we welcome you to participate in both the seminar, and our slack channel community! Zoom talks are held on Thursdays at 2:30 pm New York time. To find and join the 1W-MINDS slack channel, please click here.
Current Organizers (September 2026 - May 2027): March Boedihardjo (Michigan State University), Hung-Hsu Chou (University of Pittsburgh), Longxiu Huang (Michigan State University), Mark Iwen (Principal Organizer, Michigan State University), and Kunlun Qi (Michigan State University).
Most previous talks are on the seminar YouTube channel. You can catch up there, or even subscribe if you like.
To sign up to receive email announcements about upcoming talks, click here.
To join MINDS slack channel, click here.
Passcode: the smallest prime > 100
Data summarization arises throughout data science and scientific computing: a large dataset is replaced by a small, representative subset of its observations, called a prototype set. What makes a prototype set representative depends on the geometry used to approximate the remaining data. Discrete, linear, and conic geometries lead naturally to clustering, low-rank approximation, and nonnegative matrix factorization. We study four adaptive algorithms organized around build and swap phases, bringing together ideas that have appeared in several previously proposed methods. We present a common framework for these problems, including a power parameter $p$ that controls how approximation errors are aggregated and may require different choices across applications. Through representative case studies, we compare empirical performance, discuss implementation and computational costs, and summarize theoretical guarantees for the resulting prototype sets.
Joint work with Robert Webber and Ethan Epperly.
Classical stochastic approximation methods rely on estimators of the first moment (mean) of a random regression function. We study methods that employ estimators of both the first and the second moments, which include modern deep-learning optimizers such as Adam and Muon as special cases. We derive second-moment stochastic approximation methods through the lens of optimal preconditioning for solving matrix equations, and develop a two-stage framework for their convergence analysis. The first stage focuses on analyzing conceptual (impractical) methods that rely on the exact first and second moments. In the second stage, we replace the exact moments with their respective estimators, and invoke Dvoretzky's theorem to show that the resulting practical methods converge almost surely to a neighborhood of the target solution. The size of the neighborhood depends on the biases and variances of the first- and second-moment estimators. We derive concrete bounds for Muon and a spectral variant of Adam that determine the radius of their neighborhood of convergence.