401-3620-20L  Student Seminar in Statistics: Inference in Some Non-Standard Regression Problems

 Semester Herbstsemester 2021 Dozierende F. Balabdaoui Periodizität jedes Semester wiederkehrende Veranstaltung Lehrsprache Englisch Kommentar Maximale Teilnehmerzahl: 24Hauptsächlich für Studierende der Bachelor- und Master-Studiengänge Mathematik, welche nach der einführenden Lerneinheit 401-2604-00L Wahrscheinlichkeit und Statistik (Probability and Statistics) mindestens ein Kernfach oder Wahlfach in Statistik besucht haben. Das Seminar wird auch für Studierende der Master-Studiengänge Statistik bzw. Data Science angeboten.

Lehrveranstaltungen

NummerTitelUmfangDozierende
401-3620-00 SStudent Seminar in Statistics: Inference in Some Non-Standard Regression Problems
Remark: former title in FS 2020: Student Seminar in Statistics: Inference in Non-Classical Regression Models
2 Std.
 Mo 16:15-18:00 HG E 21 »
F. Balabdaoui

Katalogdaten

 Kurzbeschreibung Review of some non-standard regression models and the statistical properties of estimation methods in such models. Lernziel 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). Inhalt 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 regression2. Single index model3. Unlinked regression Literatur 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 Press2. "Nonparametric shape-restricted regression" by A. Guntuoyina and B. Sen, 2018, Statistical Science, Volume 33, 568-5943. "Asymptotic distributions for two estimators of the single index model" by Y. Xia, 2006, Econometric Theory, Volume 22, 1112-11374. "Least squares estimation in the monotone single index model" by F. Balabdaoui, C. Durot and H. K. Jankowski, Journal of Bernoulli, 2019, Volume 4B, 3276-33105. "Least angle regression" by B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, 2004, Annals of Statsitics, Volume 32, 407-499.6. "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, 1-197."Denoising linear models with permuted data" by A. Pananjady, M. Wainwright and T. A. Courtade and , 2017, IEEE International Symposium on Information Theory, 446-450.8. "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, 3286-33009. "Linear regression without correspondence" by D. Hsu, K. Shi and X. Sun, 2017, NIPS10. "A pseudo-likelihood approach to linear regression with partially shuffled data" by M. Slawski, G. Diao, E. Ben-David, 2019, arXiv.11. "Uncoupled isotonic regression via minimum Wasserstein deconvolution" by P. Rigollet and J. Weed, 2019, Information and Inference, Volume 00, 1-27 Voraussetzungen / Besonderes The students need to be comfortable with regression models, classical estimation methods (Least squares, Maximum Likelihood estimation...), rates of convergence, asymptotic normality, etc.

Leistungskontrolle

 Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird) Leistungskontrolle als Semesterkurs ECTS Kreditpunkte 4 KP Prüfende F. Balabdaoui Form unbenotete Semesterleistung Prüfungssprache Englisch Repetition Repetition nur nach erneuter Belegung der Lerneinheit möglich. Zulassungsbedingung Not for students who already registered for this seminar (course unit 401-3620-20L) in the Spring Semester 2020.

Lernmaterialien

 Keine öffentlichen Lernmaterialien verfügbar. Es werden nur die öffentlichen Lernmaterialien aufgeführt.

Gruppen

 Keine Informationen zu Gruppen vorhanden.

Einschränkungen

 Plätze Plätze beschränkt. Spezielles Auswahlverfahren. Belegungsbeginn Belegung ab 02.08.2021 möglich Vorrang Die Belegung der Lerneinheit ist bis 29.08.2021 nur durch die primäre Zielgruppe möglich Primäre Zielgruppe Data Science MSc (261000) Mathematik BSc (404000) ab Semester 05Statistik MSc (436000) Mathematik MSc (437000) Angewandte Mathematik MSc (437100) Mathematik (Mobilität) (448000) Warteliste Bis 27.09.2021 Belegungsende Belegung nur bis 17.09.2021 möglich

Angeboten in

StudiengangBereichTyp
Data Science MasterSeminarW
Mathematik BachelorSeminareW
Mathematik MasterSeminareW
Statistik MasterSeminar oder SemesterarbeitW