Guarantees in Machine Learning


Course basics

Logistics

  • Time: Tuesdays 10-12 CAB G59, Fridays 14-16 CHN G 42 (room changed)
  • Lectures will not be recorded! This is an in-person only class
  • Instructor: Fanny Yang, Amartya Sanyal
  • Teaching assistants:
    • Konstantin Donhauser (konstantin.donhauser at inf.ethz.ch), Jacob Clarysse (jacob.clarysse at inf.ethz.ch)
    • Office hours: upon request via email
  • Sign up on waitlist until September 27th
  • De-register until October 11th
  • E-mails will most likely not be responded to if it’s a logistical inquiry - please post privately on Moodle

We will use the following platforms

  • Please ask all of your questions in moodle, eternal gratitude from your peers is ensured ;). It will also be used for all announcements, discussion of homeworks and lectures, and parts of the assignments. If you’re still on the waitlist, you can enroll using the password Rademacher@ETH2022
  • gradescope enroll with entry code 8NXEN8 (to hand in homeworks)

Learning objectives

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

  • both easily read and write theorems that provide generalization guarantees for machine learning algorithms
  • find high-impact questions and theorems to prove and work on that you are highly passionate about

Learning objectives

  1. 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

  2. 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

  3. 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.

  4. 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.

Evaluation

  • 10% HW, 50% oral midterm, 40% project
  • Homework:
    • some graded homework problems
    • rest is self-graded with mandatory hand-in. The discrepancy between your own and our score for the selected problem will enter the final homework grade. This is to encourage you to go through the solutions carefully while self-grading.
  • Project report and presentation: see project website
  • Presence is mandatory in the last four weeks of classes during presentations

Homework information

  • Homeworks are designed to

    • do some technical (“just algebra”) work that needs to be practiced individually
    • learn how to read more material on the matter effectively (homework content will be part of the midterm exam!)

  • 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:

    • your name,
    • your Student ID, and
    • the names and IDs of any students with whom you discussed the assignment.

  • 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

Academic integrity for homeworks

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.

Schedule & course content

  • Subject to frequent changes, check back often!
  • The links to the material (handout, HW and solutions) are not active until announced in the moodle
  • The slides are not shown as is during lecture, but they contain a superset of the content of each lecture
Date Topic Location Material Assignments
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
15.11. Oral midterm TBA
16.11. Oral midterm TBA
18.11. Lecture: SQ learning CHN G 42 KV 5
22.11. No class
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
2.12. No class
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

References

Course content

Links to books are online resources free from the ETH Zurich network:

Learning Theory

Some more background reading for your general wisdom, knowledge and entertainment

Typesetting

  • For LaTeX, see 1, 2 or 3, 4.
  • For Pandoc Markdown by John McFarlane, refer to my git repo with sample instructions on how to use Pandoc for simple math notes and webpages.