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Guarantees for Machine Learning
Last Updated: 2026-02-05 15:54:27
Abstract
This course is aimed at advanced master and doctorate students who want to conduct independent research on theory for modern machine learning (ML). It teaches classical and recent methods in statistical learning theory commonly used to prove theoretical guarantees for ML algorithms. The knowledge is then applied in independent project work that focuses on understanding modern ML phenomena.
Objective
Learning objectives: - 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.
Content
This course touches upon foundational methods in statistical learning theory aimed at proving theoretical guarantees for machine learning algorithms, touching on the following topics - concentration bounds - uniform convergence and empirical process theory - high-dimensional statistics (e.g. sparsity) - regularization for non-parametric statistics (e.g. in RKHS, neural networks) - implicit regularization via gradient descent (e.g. margins, early stopping) - minimax lower bounds The project work focuses on current theoretical ML research that aims to understand modern phenomena in machine learning, including but not limited to - how overparameterization could help generalization ( RKHS, NN ) - how overparameterization could help optimization ( non-convex optimization, loss landscape ) - complexity measures and approximation theoretic properties of randomly initialized and trained NN - generalization of robust learning ( adversarial robustness, standard and robust error tradeoff, distribution shift)
Resources
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- BSC , DR , MSC
- Frequency
- Yearly recurring
Examination
- Type
- graded semester performance
Registration & Places
- Max Places
- 30
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Guarantees for Machine Learning |
|
3 h weekly |
| independent project | Guarantees for Machine Learning | No time listed | 3 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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Signal Processing and Machine Learning (The core courses and specialization courses below are a selection for students who wish to specialize in the area of "Signal Processing and Machine Learning ", see . The individual study plan is subject to the tutor's approval.)
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Specialization Courses (These specialization courses are particularly recommended for the area of "Signal Processing and Machine Learning", but you are free to choose courses from any other field in agreement with your tutor. A minimum of 40 credits must be obtained from specialization courses during the MSc EEIT.)
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Major Courses (A total of 42 CP must be achieved form courses during the Master Program. The individual study plan is subject to the tutor's approval.)
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Statistics Master (The following courses belong to the curriculum of the Master's Programme in Statistics. The corresponding credits do not count as external credits even for course units where an enrolment at ETH Zurich is not possible.)
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Doctoral Department of Computer Science (More Information at: )
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