COMS 4995-1 (“Machine Learning Theory”) is a graduate-level course on the theoretical study of algorithms for machine learning and high-dimensional data analysis. Topics include high-dimensional probability, theory of generalization and statistical learning, online learning and optimization, and spectral analysis.
In the future, this course will be called “COMS 4773”. You should be able to treat this course as a course with that number for a requirement within a CS degree program. For instance, if you have a requirement that is fulfilled by a course of the form “COMS 47xx”, then this course should count.
In this course, we won’t really discuss practical aspects of machine learning. For practice-oriented course in machine learning, see COMS 4771.
You should have a basic level of mathematical maturity and be comfortable reading and writing mathematical proofs. We’ll use a fair amount of probability and linear algebra; there’ll also be a bit of convex analysis.
You should have taken a course in machine learning (e.g., COMS 4771), or should be willing to pick up the gist of that material as we go along. This is primarily useful to understand the motivation for problems and methods we discuss in the course.
You should have taken some “advanced” (proof-based) course in mathematics, theoretical statistics, or theoretical computer science (e.g., COMS 3261, CSOR 4231).
A previous course in learning theory (e.g., COMS 4252) is not required!
If you have concerns about whether the course is suitable for you, please contact the instructor.
We plan to cover topics in generalization theory, online learning and optimization, and high-dimensional data analysis.
Topics may include:
Note that there is some overlap with COMS 42521.
Related courses on machine learning theory at other institutions:
Readings will be assigned from various sources, primarily the following texts:
Other recommended texts are:
All assignments must be submitted as PDF documents compiled using TeX, LaTeX, or similar systems with bibliographic references (e.g., using BibTeX) included as necessary.
If you have not used LaTeX before, or if you only have a passing familiarity with it, it is highly recommended that you read and complete the lessons and exercises in The Bates LaTeX Manual.
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.
You are expected to adhere to the Academic Honesty policy of the Computer Science Department, as well as the following course-specific policies.
You are welcome and encouraged to discuss homework assignments with fellow students, subject to the following rules.
Outside reference materials and sources (i.e., texts and sources beyond the assigned reading materials for the course) may be used on homework assignments only if given explicit written permission from the instructor and if the following rules are followed.
Violation of any portion of these policies will result in a penalty to be assessed at the instructor’s discretion (e.g., a zero grade for the assignment in question, a failing letter grade for the course). All violations are reported to the relevant dean’s office.
You are encouraged to use office hours and Piazza to discuss and ask questions about course material and reading assignments, and to ask for high-level clarification on and possible approaches to homework problems. If you need to ask a detailed question specific to your solution, please do so on Piazza and mark the post as “private” so only the instructors can see it.
Questions, of course, are also welcome during lecture. If something is not clear to you during lecture, there is a chance it may also not be clear to other students. So please raise your hand to ask for clarification during lecture. Some questions may need to be handled “off-line”; we’ll do our best to handle these questions in office hours or on Piazza.
Course materials (e.g., lecture slides, lecture notes, homework assignments, homework solutions, exams, exam solutions) are copyrighted and may not be re-distributed without explicit permission from the instructor.