Upcoming Events
Lecture: Nadav Dym
Tuesday, Jan. 31, 2023, 1:25 p.m. through Tuesday, Jan. 31, 2023, 2:25 p.m.
Zoom
Data Science Seminar
Nadav Dym (Technion-Israel Institute of Technology)
Registration is required to access the Zoom webinar.
A common theoretical requirement of an equivariant architecture is that it will be universal- meaning that it can approximate any continuous equivariant function. This question typically boils down to another theoretical question: assume that we have a group G acting on a set V, can we find a mapping f:V→R^m such that f is G invariant, and on the other hand f separates and two points in V which are not related by a G-symmetry? Such a mapping is essentially an injective embedding of the quotient space V/G into R^m, which can then be used to prove universality. We will review results showing that under very general assumptions such a mapping f exists, and the embedding dimension m can be taken to be 2dim(V)+1. We will show that in some cases (e.g., graphs) computing such an f can be very expensive, and will discuss our methodology for efficient computation of such f in other cases (e.g., sets). This methodology is a generalization of the algebraic geometry argument used for the well known proof of phase retrieval injectivity.
Based on work with Steven J. Gortler
Lecture: Brittany Baker
Friday, Feb. 3, 2023, 1:25 p.m. through Friday, Feb. 3, 2023, 2:25 p.m.
Walter Library 402
Industrial Problems Seminar
Brittany Baker (The Hartford)
Registration is required to access the Zoom webinar.
Lecture: Tamir Bendory
Tuesday, Feb. 7, 2023, 1:25 p.m. through Tuesday, Feb. 7, 2023, 2:25 p.m.
Zoom only
Data Science Seminar
Tamir Bendory (Tel Aviv University)
Registration is required to access the Zoom webinar.
Title: Multi-reference alignment: Representation theory perspective, sparsity, and projection-based algorithms
Abstract: Multi-reference alignment (MRA) is the problem of recovering a signal from its multiple noisy copies, each acted upon by a random group element. MRA is mainly motivated by single-particle cryo-electron microscopy (cryo-EM): a leading technology to reconstruct biological molecular structures. In this talk, I will analyze the second moment of the MRA and cryo-EM models. First, I will show that in both models the second moment determines the signal up to a set of unitary matrices, whose dimension is governed by the decomposition of the space of signals into irreducible representations of the group. Second, I will present sparsity conditions under which a signal can be recovered from the second moment, implying that the sample complexity is proportional to the square of the variance of the noise. If time permits, I will introduce a new computational framework for cryo-EM that combines a sparse representation of the molecule with projection-based techniques used for phase retrieval in X-ray crystallography.
Lecture: Margaret Holen
Friday, Feb. 10, 2023, 1:25 p.m. through Friday, Feb. 10, 2023, 2:25 p.m.
Zoom only
Industrial Problems Seminar
Margaret Holen (Princeton University)
Registration is required to access the Zoom webinar.
The finance industry offers mathematicians a rich array of career opportunities. Many of those include working with new technologies, complex data sets, and novel algorithms. Whether or not you enter the industry, we all play roles as consumers and as citizens influencing regulations.
This talk will share an overview of the finance sector, core mathematical ideas important in it, and my career path through it. My goal is to inspire you make the most of your backgrounds to shape your financial futures and the future of this industry.
Lecture: Roy Lederman
Tuesday, Feb. 14, 2023, 1:25 p.m. through Tuesday, Feb. 14, 2023, 2:25 p.m.
Zoom only
Data Science Seminar
Roy Lederman (Yale University)
Registration is required to access the Zoom webinar.
Lecture: Yuxin Chen
Tuesday, Feb. 21, 2023, 1:25 p.m. through Tuesday, Feb. 21, 2023, 2:25 p.m.
Walter Library 402
Data Science Seminar
Yuxin Chen (University of Pennsylvania)
Registration is required to access the Zoom webinar.
This talk explores the effectiveness of nonconvex optimization for noisy tensor completion --- the problem of reconstructing a low-CP-rank tensor from highly incomplete and randomly corrupted observations of its entries. While randomly initialized gradient descent suffers from a high-volatility issue in the sample-starved regime, we propose a two-stage nonconvex algorithm that is guaranteed to succeed, enabling linear convergence, minimal sample complexity and minimax statistical accuracy all at once. In addition, we characterize the distribution of this nonconvex estimator down to fine scales, which in turn allows one to construct entrywise confidence intervals for both the unseen tensor entries and the unknown tensor factors. Our findings reflect the important role of statistical models in enabling efficient and guaranteed nonconvex statistical learning.
Lecture: Brittan Farmer
Friday, Feb. 24, 2023, 1:25 p.m. through Friday, Feb. 24, 2023, 2:25 p.m.
Walter Library 402
Industrial Problems Seminar
Brittan Farmer (The Boeing Company)
Lecture: Dominique Perrault-Joncas
Friday, March 3, 2023, 1:25 p.m. through Friday, March 3, 2023, 2:25 p.m.
Walter Library 402 or Zoom
Industrial Problems Seminar
Dominique Perrault-Joncas (Amazon)
Lecture: Matt Jacobs
Tuesday, March 21, 2023, 1:25 p.m. through Tuesday, March 21, 2023, 2:25 p.m.
Walter Library 402
Data Science Seminar
Matt Jacobs (Purdue University)
Lecture: Adil Ali
Tuesday, March 28, 2023, 1:25 p.m. through Tuesday, March 28, 2023, 2:25 p.m.
Walter Library 402
Industrial Problems Seminar
Adil Ali (CH Robinson)