This course is designed to prepare Master students for successful research in ML, and prepare PhD students to find new research ideas related to ML theory. Content wise, the technical part will focus on generalization bounds using uniform convergence, and non-parametric regression.
By the end of the course
acquire enough mathematical background to understand a good fraction of theory papers published in the typical ML venues. For this purpose, students will learn common mathematical techniques from statistics and optimization in the first part of the course and apply this knowledge in the project work
critically examine recently published work in terms of relevance and determine impactful (novel) research problems. This will be an integral part of the project work and involves experimental as well as theoretical questions
find and outline an approach (some subproblem) to prove a conjectured theorem. This will be practiced in lectures / exercise and homeworks and potentially in the final project.
effectively communicate and present the problem motivation, new insights and results to a technical audience. This will be primarily learned via the final presentation and report as well as during peer-grading of peer talks.
Homeworks are designed to
No late homework
Each homework write-up must be neatly typeset as a PDF document using TeX, LaTeX, or similar systems (for more details see below). This is for you to practice getting efficient at it. Ensure that the following appear on the first page of the write-up:
Submit your write-up, one page per question, as a single PDF file by 11:59 PM of the specified due date to gradescope. Follow the instructions and mark the pages that belong to the corresponding questions. See more details on the homework sheet.
Some questions will be graded by the TAs. All questions will be self-graded by you.
Discussions on moodle
As graduates students we expect you to take this class because you want to learn the material and how to do research. All assessments are designed to maximize the learning effect. Cheating will harm yourself and hence it is of your own interest to adhere to the following policy.
All homework is submitted individually, and must be in your own words.
You may discuss only at a high level with up to two classmates; please list their IDs on the first page of your homework. Everyone must still submit an individual write-up, and yours must be in your own words; indeed, your discussions with classmates should be too high level for it to be possible that they are not in your own words.
We prefer you do not dig around for homework solutions; if you do rely upon external resources, cite them, and still write your solutions in your own words.
When integrity violations are found, they will be submitted to the department’s evaluation board.
|20.9||Lecture: Logistics, Risk decomposition||CAB G59||MW 1|
|23.9||Lecture: Concentration bounds and uniform convergence||HG E21||MW 2,3,4||HW 1|
|27.9.||Lecture: Uniform law and Rademacher complexity||CAB G59||MW 4|
|30.9.||No class||HW 1 due, HW 1 sol|
|4.10.||Lecture: Symmetrization, VC bounds, Rademacher contraction||CAB G59||MW 4||Project sign-up|
|7.10.||Interactive session: Margin bounds, structural risk minimization Margin bound (ex)||HG E21||SS 7, 26||HW 1 self-grade due, HW 2|
|11.10.||Lecture: Metric entropy||CAB G59||MW 5||De-registration deadline|
|14.10.||Lecture: Chaining, non-parametric regression, localized complexities||HG E21||MW 13||Project proposal due|
|18.10.||Lecture: From feature maps to kernels to RKHS||CAB G59||SC 4, MW 12|
|21.10.||Lecture: kernel ridge regression||CHN G42||MW 13|
|25.10.||No class||HW 2 due, HW 2 sol|
|28.10.||Interactive session: Localized Gaussian widths||CHN G 42|
|1.11.||Lecture: Minimax lower bounds||CAB G59||MW 14, MW 15||HW 2 self-grade due, HW 3|
|4.11.||Lecture: PAC learning I (Definition and examples)||CHN G 42||KV 1, SD 2|
|8.11.||Lecture: PAC learning II (Efficiency and tradeoff)||CAB G59||KV 1,2,3, SD 8|
|11.11.||Interactive session: PAC learning||CHN G 42||HW 3 due, HW 3 sol|
|18.11.||Lecture: SQ learning||CHN G 42||KV 5|
|25.11.||Lecture: Implicit bias, Slides||CHN G 42)||Mid-Project drafts due|
|29.11.||Lecture: Random design, Overparameterization and double descent||CAB G59||HW 3 self-grade due|
|6.12.||Project feedback||CAB G59|
|9.12.||[Presentations 1], see full schedule||CHN G 42|
|13.12.||[Presentations 2], see full schedule||CAB G59|
|16.12.||[Presentations 3], see full schedule|
|20.12.||[Presentation 4], see full schedule||[Peer-grading due]|
|12.1.||No class||Project reports due|
Links to books are online resources free from the ETH Zurich network:
Martin Wainwright: High-dimensional statistics (core reference for the course)
Steinwart and Christmann: Support Vector Machines: more mathematical treatment of RKHS
Michael Kearns and Umesh Vazirani: An introduction to computational learning theory: (Important material for PAC/SQ learning)
Some more background reading for your general wisdom, knowledge and entertainment
Keener: Theoretical Statistics: e.g. asymptotic optimality (MLE), UMVU testing