ACMD Seminar: Missing Data and Likelihood Geometry

John Cobb
Ph.D. Candidate, Dept. of Mathematics, Univ. Wisconsin-Madison

Tuesday, March 26, 2024, 3:00-4:00 PM ET (1:00-2:00 PM MT)

In person at: Boulder 1-1107 with VTC to Gaithersburg Bldg. 101 LR D
Online at: ZoomGov

Add this talk to your calendar: https://inet.nist.gov/calendar/ics/2278736

Abstract: The talk will review two recent but very different projects. In the first half, I’ll describe how spectral graph theory has been generalized using the sheaf Laplacian and how we used this theory to make predictions on knowledge graphs in the presence of large amounts of missing data. In the second half, I will show how characteristics of the maximum likelihood estimation (MLE) problem are reflected in the geometry of the likelihood correspondence, a variety that ties together data and their maximum likelihood estimators. I’ll show how to construct the vanishing ideal of the likelihood correspondence for the large class of toric models and find a Gröbner basis in the case of complete and joint independence models arising from multi-way contingency tables. These results provide insight into their properties and offer faster computational strategies for solving the MLE problem.

Bio:  John Cobb is a fifth-year PhD student studying mathematics at the University of Wisconsin-Madison, and will be an NSF postdoctoral fellow with Hal Schenck at Auburn starting in the Fall. His research interests are primarily within algebraic geometry and commutative algebra, and his work involves syzygies, toric varieties, defining equations of curves, and more recently, applications to data science. He is interested in leveraging new developments within algebraic geometry to address optimization problems and dimensionality reduction. 

Host: Zach Grey

Note: This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

Note: Visitors from outside NIST must contact Meliza Lane at least 24 hours in advance.