Times: Tuesday and Thursday, 9:30-10:45 am
Location: Klaus Advanced Computing building, room 1456
Instructor: Vidya K Muthukumar (vmuthukumar8@gatech.edu)
TAs: Jamshid Hassanpour (jhassanpour3@gatech.edu) and Yihan Liu (yliu3470@gatech.edu)
Office Hours: [Instructor] Tuesdays 4-5 pm Groseclose 303, Thursdays 11 am-12 pm Coda 1106 Briarcliff
[TA] once a week, TBD
Prerequisites: There are no formal prerequisites. However, I expect students to have exposure to basic linear algebra and probability, and have basic programming skills. Mathematical and proof-based arguments will be extensively used throughout the course. Having taken a rigorous, proof-based undergraduate course will prove very helpful. We will try our best to bring you up to speed with some of the prerequisites by using some auxiliary handouts, reviews during lecture, and optional Homework 0.
Brief description: The purpose of this course is to provide first year PhD students in engineering and computing with a solid mathematical background for two of the pillars of modern machine learning, data science, and artificial intelligence: linear algebra and applied probability. This is a foundational mathematical introduction to machine learning and does not engage with applications of deep learning/large language models.
Upon successful completion of the course, you will have learned:
(a) The linear algebraic principles behind modeling function classes, with exposure to both finite and infinite dimensional modeling techniques.
(b) The probabilistic principles based on which we can perform statistical estimation with our models given data.
(c) Some basic principles that govern the design and analysis of optimization algorithms used to fit models to data.
The most important takeaway for some of you might be to recognize that these ideas can help in designing new, principled machine learning methodology, or conversely, to recognize the immense opportunity that exists to place several modern machine learning techniques on a rigorous footing.
Grading/Format: The course will be graded as follows:
- Homeworks (top 5/6): 50%
- Midterm (in class, tentative date Oct 2): 25%
- Final exam (Dec 11 8 am): 25%
Piazza/Canvas: The primary mode of interactive communication in this course will be Piazza. Please sign up at the course page, and monitor Piazza for announcements regarding lecture, homeworks, midterm and final. As is standard, we will also use Canvas to keep track of assignments and share resources related to the class.
Lecture schedule (tentative, subject to change)
| Date | Topic | Resources |
| 19 Aug | Logistics and introduction | Lecture slides |
| 21 Aug | Introduction to linear representations | Lecture note |
| 26 Aug | Linear algebra basics | Lecture note |
Homework schedule:
Submission due date and self-grade upload deadline are both 11:59 ET. Submission and self-grade upload will be done via Canvas.
| Rough set of topics | Upload date | Due date | Self-grade due date | |
| Homework 0 (optional) | Review | 19 Aug | 26 Aug | N/A |