401-4627-DRL  Empirical Process Theory and Applications

SemesterSpring Semester 2022
LecturersS. van de Geer
Periodicitynon-recurring course
Language of instructionEnglish
CommentOnly for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger (Link) with the course number. The email should have the subject „Graduate course registration (ETH)“.


401-4627-00 VEmpirical Process Theory and Applications2 hrs
Wed08:15-10:00HG D 5.2 »
S. van de Geer

Catalogue data

AbstractEmpirical process theory provides a rich toolbox for studying the properties of empirical risk minimizers, such as least squares and maximum likelihood estimators, support vector machines, etc.
ContentIn this series of lectures, we will start with considering exponential inequalities, including concentration inequalities, for the deviation of averages from their mean. We furthermore present some notions from approximation theory, because this enables us to assess the modulus of continuity of empirical processes. We introduce e.g., Vapnik Chervonenkis dimension: a combinatorial concept (from learning theory) of the "size" of a collection of sets or functions. As statistical applications, we study consistency and exponential inequalities for empirical risk minimizers, and asymptotic normality in semi-parametric models. We moreover examine regularization and model selection.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits2 credits
ExaminersS. van de Geer
Typeungraded semester performance
Language of examinationEnglish
RepetitionRepetition only possible after re-enrolling for the course unit.

Learning materials

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No information on groups available.


PriorityRegistration for the course unit is only possible for the primary target group
Primary target groupDoctorate Mathematics (439002)
Doctorate Computational Science and Engineering (439102)

Offered in

Doctorate MathematicsGraduate SchoolWInformation