Tuesday, Sept. 26, 2023, 1:25 p.m. through Tuesday, Sept. 26, 2023, 2:25 p.m.
Lind Hall 325 or Zoom
Data Science Seminar
Wuchen Li (University of South Carolina)
We study the Lyapunov convergence analysis for degenerate and non-reversible stochastic differential equations (SDEs). We apply the Lyapunov method to the Fokker-Planck equation, in which the Lyapunov functional is chosen as a weighted relative Fisher information functional. We derive a structure condition and formulate the Lypapunov constant explicitly. Given the positive Lypapunov constant, we prove the exponential convergence result for the probability density function towards its invariant distribution in the L1 norm. Several examples are presented: underdamped Langevin dynamics with variable diffusion matrices, quantum SDEs in Lie groups (Heisenberg group, displacement group, and Martinet sub-Riemannian structure), three oscillator chain models with nearest-neighbor couplings, and underdamped mean field Langevin dynamics (weakly self-consistent Vlasov-Fokker-Planck equations).
Friday, Sept. 22, 2023, 1:25 p.m. through Friday, Sept. 22, 2023, 2:25 p.m.
Industrial Problems Seminar
Morteza Mardani (NVIDIA Corporation)
In the rapidly evolving landscape of AI, a transformative shift from content retrieval to content generation is underway. Central to this transformation are diffusion models, wielding remarkable power in visual data generation. My talk touches upon the nexus of generative AI and NVIDIA's influential role therein. I will then navigate through diffusion models, elucidating how they establish the bedrock for leveraging foundational models. An important question arises: how to integrate the rich prior of foundation models in a plug-and-play fashion for solving downstream tasks such as inverse problems and parametric models? Through the lens of variational sampling, I present an optimization framework for sampling diffusion models that only needs diffusion score evaluation. Not only does it provide controllable generation, but the framework also establishes a connection with the well-known regularization by denoising (RED) framework, unveiling its extensive implications for text-to-image/3D generation.
Friday, Sept. 15, 2023, 1:25 p.m. through Friday, Sept. 15, 2023, 2:25 p.m.
Lind Hall 325 or Zoom
Industrial Problems Seminar
Miles Crosskey (CoVar Applied Technologies)
Long COVID, a condition characterized by persistent symptoms following COVID-19 infection, poses challenges in identification due to its diverse manifestations and novelty. Leveraging the N3C Enclave's electronic health record (EHR) data, we devised a machine learning method to construct a computable phenotype for Long COVID. This approach enables the identification of individuals with this condition through EHR data. Our model demonstrates a sensitivity of 72.7% and a specificity of 96.3%, maintaining consistent performance on held-out sites. This technique contributes to a better understanding of Long COVID's prevalence and impact.
Tuesday, Sept. 12, 2023, 1:25 p.m. through Tuesday, Sept. 12, 2023, 2:25 p.m.
Lind Hall 325 and Zoom
Data Science Seminar
Jona Lelmi (University of California, Los Angeles)
The MBO scheme is a highly performant scheme used for data clustering. Given some data, one constructs the similarity graph associated to the data points. The goal is to split the data into meaningful clusters. The algorithm produces the clusters by alternating between diffusion on the graph and pointwise thresholding. In this talk I will present the first theoretical studies of the scheme in the large data limit. We will see how the final state of the algorithm is asymptotically related to minimal surfaces in the data manifold and how the dynamics of the scheme is asymptotically related to the trajectory of steepest descent for surfaces, which is mean curvature flow. The tools employed are variational methods and viscosity solutions techniques. Based on joint work with Tim Laux (U Bonn).
Friday, Sept. 8, 2023, 1:25 p.m. through Friday, Sept. 8, 2023, 2:25 p.m.
Industrial Problems Seminar
Michael Viscardi (Helm.ai)
Helm.ai develops scalable AI software for autonomous driving, robotics, and other applications. This talk will give an overview of our technology and results.
Monday, June 19, 2023, 8 a.m. through Friday, July 28, 2023, 5 p.m.
The Math-to-Industry Boot Camp is an intense six-week session designed to provide graduate students with training and experience that is valuable for employment outside of academia. The program is targeted at Ph.D. students in pure and applied mathematics. The boot camp consists of courses in the basics of programming, data analysis, and mathematical modeling. Students work in teams on projects and are provided with training in resume and interview preparation as well as teamwork.
There are two group projects during the session: a small-scale project designed to introduce the concept of solving open-ended problems and working in teams, and a "capstone project" that is posed by industrial scientists. Recent industrial sponsors included Cargill, Securian Financial and CH Robinson. Weekly seminars by speakers from many industry sectors provide the students with opportunities to learn about a variety of possible future careers.
Evaluating the real-world safety and robustness of deep learning models
Charles Godfrey, Pacific Northwest National Laboratory
Henry Kvinge, Pacific Northwest National Laboratory
Team: Kean Fallon, Iowa State University; Aidan Lorenz, Vanderbilt University; Jessie Loucks-Tavitas, University of Washington; Sandra Annie Tsiorintsoa, Clemson University; Benjamin Warren, Texas A&M University
Abstract: Deep learning has shown remarkable capabilities in a range of important tasks, but at the same time has also been shown to be brittle in many ways, especially in real-world deployed environments. This can range from a language model that can be triggered to insult users to a vision model that doesn’t recognize machine parts in certain lighting conditions. Understanding how a model will behave at deployment is a serious problem in real-world AI and requires a mixture of mathematical and out-of-the-box thinking. In this capstone project, participants will be asked to evaluate models delivered to a client by 3rd party vendors from the perspective of overall robustness. This will include (i) evaluating how well a model performs outside of its test set and (ii) particular failure modes of the model that should be avoided. The final project deliverable will include a short report recommending for or against proceeding with use of the model in the client’s application.
Interpolating the Implied Volatility Surface
Chris Bemis, X Cubed Capital Management
Team: Qinying Chen, University of Delaware; Nellie Garcia, University of Minnesota; Emily Gullerud, University of Minnesota; Shaoyu Huang, University of Pittsburgh; Pascal Kingsley (PK) Kataboh, University of Delaware; Matthew Williams, Colorado State University
Abstract: Financial markets price volatility in underlying securities primarily through what are called options. These options are defined by reference to their payoffs and the date at which they expire, along with other features such as prevailing rates, the underlying security price, and so on. The result is that markets reference a surface of implied volatilities based on market prices.
In this project, we will fit such surfaces in financially meaningful ways; especially focusing on the preclusion of arbitrage opportunities in the resulting interpolation. These methods are critical in creating assessments of constant expiry volatility time series amongst many other applications. They also sometimes suffer from a lack of stability in parameter estimation as new surfaces are fit.
We will use real (and noisy) data with the goal of efficiently creating stable volatility surface interpolations and time series of constant expiry volatility.
Multimodal Search in eCommerce
Christopher Miller, eBay
Team: Tanuj Gupta, Texas A&M University; Meagan Kenney, University of Minnesota; Pavel Kovalev, Indiana University; Chiara Mattamira, University of Tennessee; Jeremy Shahan, Louisiana State University; Hannah Solomon, Texas A&M University
Abstract: In classical search, most or all user interfaces are text-based. Users submit queries made up of strings, and possibly assert filters (also text-based) to limit the result set. When a user does not like their results, they can “requery” with slightly different terms to produce better results. This process continues until the user is satisfied or gives up.
In visual search, users submit images for their queries. The query images might come from the internet, other eCommerce sites, or from the users’ own library. They expect to see results that look similar to their query image. If the user does not like their results, now they’re stuck: they cannot simply tweak an image the way they can tweak a text-based query.
This is the problem we will resolve with a two-phase multimodal search. The first phase is regular visual search. In the second phase, users can add text to their query to augment their search results. For example, they submit a photo of a yellow dress they have at home, but add the text “green dress” to get results that are green, but otherwise similar to the dress they already have. This enables users to iteratively improve their search results just like they would in classical search.
An Excess Demand Model of Home Price Appreciation
Christopher Jones, US Bank
Matt Mansell, US Bank
Leo Digiosia, US Bank
Team: Ismail Aboumal, California Institute of Technology; Daniela Beckelhymer, University of Minnesota; Jarrad Botchway, Missouri University of Science and Technology; Jordan Pellett, University of Tennessee; Marshall Smith, University of Minnesota
Abstract: National home prices in the U.S. are tracked by one of a few indices: the Case-Shiller and FHFA home price indices being the most popular. Home price appreciation is an important metric tracked by commercial banks. Because bank originators have the ability to hold mortgages on their balance sheets, refinance activity such as cash-out and rate/term refinance contribute to the interest rate and macroeconomic risk of these assets. Traditionally, home prices are forecasted using a form of econometric regression where multiple correlated variables are used in a model. However, these models often lead decision-makers in a bank lacking in terms of interpretability or insights into the mortgage market. In this project, we will explore home prices from the point of view of a differential equation so that we can obtain forecasted values of home price appreciation on a variety of time scales. We will explore the conceptual soundness of a model of excess demand and quantify uncertainty around parameter estimation and shape optimization. We will create a story around this model to explain past events and potential future scenarios.
Monday, June 5, 2023, 8 a.m. through Friday, June 16, 2023, 5 p.m.
School of Mathematics
Vincent Hall, 206 Church St. SE
Minneapolis, MN 55455
Applications due April 30.
- This summer program aims to promote the studies and research activities on random optimizations in complex systems for Minnesota's local undergraduate students.
- The workshop will cover a wide range of subjects and tools in probability theory and mathematical physics, especially addressing their applications in machine learning, data science, and imaging processing.
- During the 10-day program, students are expected to attend two daily lecture sessions and a group problem session. Additional professional development sessions will discuss graduate school and careers in related fields.
- Upon completion, students will receive a certificate issued by the School of Mathematics at the University of Minnesota.
Who can apply
Undergraduate students from Minnesota's local colleges and universities.
Introductory Probability, Linear Algebra, and Basic Properties of Differential Equations
Week 1: June 5-9
|9-10:15am||Wei-Kuo Chen||Statistical Physics and Random Optimizations|
|10:45am-12pm||Arnab Sen||Clustering and Community Detection|
|1:30-3:30pm||Ratul Biswas||Discussion and Problem Session|
Week 2: June 12-16
|9:00-10:15am||Rishabh Dudeja||Universality in High-Dimensional Optimization and Statistics Detection|
|10:45am-12:00pm||Wonjun Lee||Introduction to Computational Optimal Transport|
|1:30-3:30pm||Heejune Kim||Discussion and Problem Session|
- A brief CV
- A short recommendation letter from a professor
- Personal statement describing scientific interests and course preparations for this workshop
When filling in the Application Form, please only select either "Local expenses (hotel and meals)" or "Not requesting funding."
The participants will receive either a fixed per diem or a meal plan to cover food. Support is available for students in need of on-campus lodging during the program.
Wei-Kuo Chen (University of Minnesota)
This program is financially supported by the National Science Foundation and Institute for Mathematics and Its Applications.
Monday, May 22, 2023, 8 a.m. through Friday, May 26, 2023, Noon
University of Minnesota, Twin Cities
- Jim Fowler — The Ohio State University
- Duane Nykamp — University of Minnesota, Twin Cities
- Matt Thomas — Cornell University
In this five-day workshop, participants will learn how to create and implement online learning experiments using the Distributed Open Education Network (Doenet, doenet.org). Doenet is designed to help faculty critically evaluate how different content choices influence student learning in their classrooms. Doenet enables instructors to quickly test hypotheses regarding the relative effectiveness of alternative approaches by providing tools to assign different variations of an activity and analyze the resulting data.
Following brief introductions and demos of features of the Doenet platform, participants will work in small groups to develop learning experiments that can be used in the college classroom, assisted by the developers of Doenet. The expectation is that participants will leave the workshop with a learning experiment that they can use in their classroom the following year.
The workshop will run from 9 AM on Monday, May 22 through 4 PM on Friday, May 26. All organized activities will occur between 9 AM and 4 PM each day.
The workshop is open to faculty at all levels teaching STEM courses.
To apply, please submit the following documents through the Program Application link at the top of the page:
- A personal statement briefly (200 words or less) stating what you hope to contribute to the discussion on learning experiments and what you hope to gain from this workshop. Include courses you teach for which you'd like to develop learning experiments. Priority will be given to those able to run learning experiments in their courses in the following year.
- A brief CV or resume. (A list of publications is not necessary.)
This workshop is fully funded by the National Science Foundation. All accepted participants who request funding for travel and/or local expenses will receive support. There is no registration fee.
Participants who perform learning experiments on Doenet during the following academic year will be eligible to receive a small stipend to support their work.
Deadline for full consideration: April 17, 2023.
Supported by NSF grant DUE 1915363.
Tuesday, May 2, 2023, 1:25 p.m. through Tuesday, May 2, 2023, 2:25 p.m.
Walter Library 402 or Zoom
Data Science Seminar
Elad Romanov (Stanford University)
Principal Component Analysis (PCA) is a fundamental and ubiquitous tool in statistics and data analysis.
The bare-bones idea is this. Given a data set of n points y_1, ..., y_n, form their sample covariance S. Eigenvectors corresponding to large eigenvalues--namely directions along which the variation within the data set is large--are usually thought of as "important" or "signal-bearing"; in contrast, weak directions are often interpreted as "noise", and discarded along the proceeding steps of the data analysis pipeline. Principal component (PC) selection is an important methodological question: how large should an eigenvalue be so as to be considered "informative"?
Our main deliverable is ScreeNOT: a novel, mathematically-grounded procedure for PC selection. It is intended as a fully algorithmic replacement for the heuristic and somewhat vaguely-defined procedures that practitioners often use--for example the popular "scree test".
Towards tackling PC selection systematically, we model the data matrix as a low-rank signal plus noise matrix Y = X + Z; accordingly, PC selection is cast as an estimation problem for the unknown low-rank signal matrix X, with the class of permissible estimators being singular value thresholding rules. We consider a formulation of the problem under the spiked model. This asymptotic setting captures some important qualitative features observed across numerous real-world data sets: most of the singular values of Y are arranged neatly in a "bulk", with very few large outlying singular values exceeding the bulk edge. We propose an adaptive algorithm that, given a data matrix, finds the optimal truncation threshold in a data-driven manner under essentially arbitrary noise conditions: we only require that Z has a compactly supported limiting spectral distribution--which may be a priori unknown. Under the spiked model, our algorithm is shown to have rather strong oracle optimality properties: not only does it attain the best error asymptotically, but it also achieves (w.h.p.) the best error--compared to all alternative thresholds--at finite n.
This is joint work with Matan Gavish (Hebrew University of Jerusalem) and David Donoho (Stanford).
Friday, April 28, 2023, 1:25 p.m. through Friday, April 28, 2023, 2:25 p.m.
Walter Library 402 or Zoom
Industrial Problems Seminar
Sriharsha (Harsha) Veeramachaneni (WindLogics)
The simplified tutorial-style talk will delve into the fundamentals of how electricity is transacted in the north-American grid: How electricity prices are determined; How the physics of electricity flow affects prices, and some counterintuitive consequences thereof; And how all this relates to the business of profitably operating a power plant.