COMS 4773 is a graduate-level introduction to machine learning theory.
See the Course Webpage for more logistical information (e.g., office hours) and announcements.
Mathematical theorems about machine learning algorithms and problems are tools for engaging in rigorous scientific inquiry about machine learning. Such theorems provide evidence of understanding and serve to communicate ideas with clarity and precision.
The goal of this course (COMS 4773) is to equip students with tools to:
(Note: In this course, we won’t really discuss application-oriented aspects of machine learning; those aspects can be found in courses like COMS 4771.)
Students should have mathematical maturity and be comfortable reading and writing mathematical proofs. We’ll use a fair amount of probability and linear algebra (both at an undergraduate level); there’ll also be a bit of convex analysis and algorithmic design and analysis (but not at a very advanced level).
Students should have taken some advanced proof-based course in mathematics, theoretical statistics, or theoretical computer science.
A course in machine learning (e.g., COMS 4771) is useful for understanding the motivation behind some problems and methods we discuss in this course, but it is not required.
Please contact the instructor with any concerns about the prerequisites.
A tentative list of topics is as follows.
The Spring 2024 and Spring 2020 editions of this course covered similar topics.
There is a lot of overlap with COMS 4252 and STAT 6203.
We won’t directly follow any textbook, but the following may be useful references:
Students are expected to complete reading assignments, attend lectures and take careful notes.
There are no make-up exams or make-up assignments available.
If you require accommodations or support services from Disability Services, please make necessary arrangements in accordance with their policies within the first two weeks of the semester.
All problem set write-ups must be submitted as PDF documents compiled using LaTeX or similar mathematical typesetting systems. The lessons and exercises in The Bates LaTeX Manual are useful for students who would like to use LaTeX but only have a passing familiarity with it.
Students are encouraged to discuss the course material and the problem sets with each other in small groups. However, it is strongly recommended to make a serious attempt on the problem sets individually before consulting with others.
Problem set write-ups must be done individually, without looking at another student’s write-up, whether in part or in full. The write-ups must explicitly declare: (1) any use of “external sources” beyond the course lectures and assigned reading (e.g., lecture notes from other courses, research papers, textbooks, Wikipedia articles); (2) any discussions with other students about problem sets; (3) any “discussions” with AI tools about the problem sets (but see below about the AI policy).
Students will also engage in peer evaluation of problem sets, to practice checking and evaluating mathematical arguments that may or may not be valid. Peer evaluation must be done individually.
The purpose of the exams (i.e., midterm and final) is to assess whether students have been following the course material. The difficulty of the exam problems should be well below that of the (typical) problem sets.
Exams are closed-book, closed-notes, device-free, AI-free, etc.
Students are required to adhere to the Academic Honesty policy of the Computer Science Department.
Exams (i.e., midterm and final) must be completed individually. Collaboration or discussion between students on exams is not permitted. Exams are closed-book, closed-notes, device-free, AI-free, etc.
See also the Office of the Provost’s Generative AI Policy.