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401-3620-20L 4 Credits BSC , MSC D-ITET , D-INFK , D-MATH
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Student Seminar in Statistics: Inference in Some Non-Standard Regression Problems

Lecturers & Examiners: Prof. Dr. Fadoua Balabdaoui
Number of participants limited to 24. Mainly for students from the Mathematics Bachelor and Master Programmes who, in addition to the introductory course unit 401-2604-00L Probability and Statistics, have heard at least one core or elective course in statistics. Also offered in the Master Programmes Statistics resp. Data Science.
VVZ CR n/a

Last Updated: 2026-06-01 11:33:15

Abstract

Review of some non-standard regression models and the statistical properties of estimation methods in such models.

Objective

The main goal is the students get to discover some less known regression models which either generalize the well-known linear model (for example monotone regression) or violate some of the most fundamental assumptions (as in shuffled or unlinked regression models).

Content

Linear regression is one of the most used models for prediction and hence one of the most understood in statistical literature. However, linearity might be too simplistic to capture the actual relationship between some response and given covariates. Also, there are many real data problems where linearity is plausible but the actual pairing between the observed covariates and responses is completely lost or at partially. In this seminar, we review some of the non-classical regression models and the statistical properties of the estimation methods considered by well-known statisticians and machine learners. This will encompass: 1. Monotone regression 2. Single index model 3. Unlinked regression

Resources

Literature

In the following is the tentative material that will be read and studied by each pair of students (all the items listed below are available through the ETH electronic library or arXiv). Some of the items might change. 1. Chapter 2 from the book "Nonparametric estimation under shape constraints" by P. Groeneboom and G. Jongbloed, 2014, Cambridge University Press 2. "Nonparametric shape-restricted regression" by A. Guntuoyina and B. Sen, 2018, Statistical Science, Volume 33, 568-594 3. "Estimating a Convex Function in Nonparametric Regression" by M. Birke and H. Dette, 2007, Scandinavian Journal of Statistics, Volume 34, 384-404. 4. "Locally adaptive regression splines" by E. Mammen and S. van de Geer, 1997, Annals of Statistics, Volume 25, 387–413 5. "Least squares estimation in the monotone single index model" by F. Balabdaoui, C. Durot and H. K. Jankowski, Journal of Bernoulli, 2019, Volume 4B, 3276-3310 6. "Semiparametric efficiency in convexity constrained single-index model" by A. Kuchibhotla, R. Patra and B. Sen, Journal of the American Statistical Association, 2021, Volume 118, 272–286 7. "Sharp thresholds for high dimensional and noisy sparsity recovery using l1-constrained quadratic programming (Lasso)" by M. Wainwright, 2009, IEEE transactions in Information Theory, Volume 55, 1-19 8."Linear regression with shuffled data: statistical and computation limits of permutation recovery" by A. Pananjady, M. Wainwright and T. A. Courtade , 2018, IEEE transactions in Information Theory, Volume 64, 3286-3300 9. "Linear regression without correspondence" by D. Hsu, K. Shi and X. Sun, 2017, NIPS 10. "Linear Regression With Unmatched Data: A Deconvolution Perspective" by M. Azadkia and F. Balabdaoui, 2024, Journal of Machine Learning Research, Volume 25, 1−55, 2024 11. "Permuted and Unlinked Monotone Regression in $R^d$: an approach based on mixture modeling and optimal transport" by M. Slawski and B. Sen, 2024, Journal of Machine Learning Research, Volume, 25, 1-57

General Information

Language
English
Levels
BSC , MSC
Frequency
Semesterly recurring

Examination

Type
ungraded semester performance

Registration & Places

Limited places (Special selection)
Signup End
08.02.2025
Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
seminar Student Seminar in Statistics: Inference in Some Non-Standard Regression Problems
Fully booked.
  • Mon 16:15-18:00 (HG E 22)
2 h weekly

Offered In

  • Mathematik Bachelor
    • Seminare (ZUR BEACHTUNG: Damit die Zuteilung der verfügbaren Seminarplätze sich nicht primär auf den Zeitpunkt des Einschreibens in die Warteliste stützen muss, haben die meisten Mathematik-Seminare ein spezielles Auswahlverfahren. Eine direkte Belegung in myStudies ist dann nicht möglich, alle kommen zuerst auf die Warteliste. Ausserdem gilt: Die Auswahl an Mathematik-Seminaren wird auf 1 Seminar pro Semester beschränkt. Beachten Sie auch die Lerneinheit 401-0002-99L Generic Seminar - Second Priority / Third Priority.)
  • Mathematik Master
    • Seminare und Semesterarbeiten
      • Seminare (ZUR BEACHTUNG: Damit die Zuteilung der verfügbaren Seminarplätze sich nicht primär auf den Zeitpunkt des Einschreibens in die Warteliste stützen muss, haben die meisten Mathematik-Seminare ein spezielles Auswahlverfahren. Eine direkte Belegung in myStudies ist dann nicht möglich, alle kommen zuerst auf die Warteliste. Ausserdem gilt: Die Auswahl an Mathematik-Seminaren wird auf 1 Seminar pro Semester beschränkt. Falls Sie in diesem Semester 2 Seminare absolvieren müssen, melden Sie sich bitte beim Studiensekretariat (E-Mail: ). Beachten Sie auch die Lerneinheit 401-0002-99L Generic Seminar - Second Priority / Third Priority.)
  • Statistik Master (Die hier aufgelisteten Lehrveranstaltungen gehören zum Curriculum des Master-Studiengangs Statistik. Die entsprechenden KP gelten nicht als Mobilitäts-KP, auch wenn gewisse Lerneinheiten nicht an der ETH Zürich belegt werden können.)
  • Data Science Master