MATH 7870-001 — Randomized NLA for Data Science and Machine Learning
Spring 2026
| Instructor: |
Akil Narayan |
| Email: |
akil sci.utah.edu |
| Office phone: |
+1 801-581-8984 |
| Office location: |
WEB 4666, LCB 116 |
| Office hours: |
Tuesday 9:45-10:40am in LCB 116, or by appointment |
| Class meeting time: |
Tuesday, Thursday 10:45am - 12:05pm |
| Class meeting location: |
M LI 1735 |
This course is a gentle journey through the land of randomized methods, focused on core (numerical) linear algebra tasks, and if time permits with some exploration of stochastic optimization methods.
The course syllabus is here: PDF
The content of this course is split across this website and Canvas. The material available on this website is:
- Course syllabus
- Homework assignments
- Lecture slides
- Miscellaneous handouts and resources
The material available on Canvas is:
- Course syllabus
- Homework assignments and submission portal
- Grades
In-class presentations have the schedule below.
NOTE: There are 3 slots per day. All classes are in-person, except Tues April 7, which will be over Zoom. A link will be advertised via email and also posted as a Canvas announcement.
| Date |
Presenter |
|
Resources |
Topic |
| Thursday, April 2 |
Zane C. |
|
Ref |
Trace estimation (XTrace) |
|
Tory R. |
|
Ref |
Fast Randomized Iteration |
|
Gaurav D. |
|
|
|
| Tuesday, April 7 |
Anwesa D. |
ZOOM |
Ref |
Iterative Hessian Sketch |
|
Tim S. |
ZOOM |
Ref |
Fast direct methods for Gaussian processes |
|
Laurel W. |
ZOOM |
Ref |
Sparse Randomized Kaczmarz for EEG Signals |
|
— |
ZOOM |
|
|
| Thursday, April 9 |
Lucy L. |
|
Ref |
Randomized Cholesky-QR factorizations |
|
Asher M. |
|
|
|
|
Justin S. |
|
Ref |
Stochastic matrix inversion |
| Tuesday, April 14 |
Erin S. |
|
Ref |
Matrix sketching for linear mixed models |
|
Zijie L. |
|
Ref |
Sharp analysis of low-rank kernel matrix approximations |
|
Valeria S. |
|
Ref 1, Ref 2 |
Sampling the Unseen: Importance Weighting for Latent Confounders |
| Thursday, April 16 |
Joel K. |
|
Ref |
Stochastic reformulations of linear systems |
|
Parikshita G. |
|
|
|
|
Nicole L. |
|
|
|
|
David R. |
|
|
|
| Tuesday, April 21 |
Eli F. |
|
Ref |
Trace estimation (Hutch++) |
|
Shridhar V. |
|
Ref |
Randomly pivoted Cholesky |
|
John T. |
|
Ref |
Recursive Sampling for the Nyström methods |
Graded assignments
Individual grades for each assignment will be posted to Canvas. (uNID login required.) Note that the letter grades appearing on Canvas are not representative of predicted final letter grades for the course. Final letter grades will be computed according to the rubric and policies on the syllabus.
Miscellaneous handouts
The following are slides from class.
|
Description
|
Posting date
|
Download
|
Marked document
|
|
Presentation information and a non-comprehensive list of papers
|
March 4, 2026
|
PDF
|
|
|
00: Course overview
|
January 03, 2026
|
PDF
|
|
|
01: An intro to numerical linear algebra
|
January 07, 2026
|
PDF
|
PDF
|
|
02: A review of probability
|
January 12, 2026
|
PDF
|
PDF
|
|
03: Matrix multiplication: preasymptotic estimation
|
January 19, 2026
|
PDF
|
PDF
|
|
04: Scalar concentration
|
January 26, 2026
|
PDF
|
PDF
|
|
05: Applications of scalar concentration
|
February 2, 2026
|
PDF
|
PDF
|
|
06: Matrix concentration: Initial results
|
February 13, 2026
|
PDF
|
PDF
|
|
07: Matrix concentration: Matrix Chernoff
|
February 25, 2026
|
PDF
|
PDF
|
|
08: Matrix concentration: Matrix Bernstein
|
March 2, 2026
|
PDF
|
PDF
|
|
09: Random embeddings
|
March 24, 2026
|
PDF
|
PDF
|
|