Statistics research seminar

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Spring Semester 2020

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Speaker

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9 March 2020
14:15-15:00

Cancelled ! Shahar Mendelson
Mathematical Sciences Institute, Australian National University

Event Details

Research Seminar in Statistics

Title	Cancelled !! On the geometry of random polytopes and the small-ball method
Speaker, Affiliation	Cancelled ! Shahar Mendelson, Mathematical Sciences Institute, Australian National University
Date, Time	9 March 2020, 14:15-15:00
Location	HG G 19.1
Abstract	Let X be an isotropic random vector in R^n and let X_1,...,X_N be independent copies of X for N>cn. A well known question in Asymptotic Geometric Analysis that has been studied extensively over the last 30 years is whether (and under what conditions) the symmetric convex hull of X_1,...,X_N, absconv(X_1,...,X_N), contains a large canonical convex body. The first breakthrough was in the late 80's, when Gluskin showed that if X is the standard Gaussian vector, then with high probability, absconv(X_1,...,X_N) contains c\sqrt{log(N/n)}B_2^n. Results of a similar flavour (and what "similar flavour" means here will be explained in the talk) are known, for example, when X has iid subgaussian coordinates and when X is log-concave. All these results rely on X exhibiting enough concentration and the arguments break down when X is no longer (very) light-tailed. We present a general approach to the problem that is based on the small-ball method and show that under minimal conditions on X, absconv(X_1,...,X_N) contains the dual of a natural floating body associated with X. This leads to a unified proof of all the previous results and allows one to address the problem when X is heavy-tailed. At the heart of the proof is an idea that is used frequently in the analysis of many statistical recovery procedures: obtaining a high probability, lower bound on the infimum of a nonnegative random process - in this case, on \inf_{t \in T} \\|\Gamma t\\|_\infty, where T is an appropriate subset of R^n, and \Gamma is the random matrix whose rows are X_1,...,X_N. A joint work with O. Guedon, F. Krahmer, Christian Kummerle and Holger Rauhut.

Cancelled !! On the geometry of random polytopes and the small-ball methodread_more (CANCELLED)

HG G 19.1

27 March 2020
14:00-14:45

cencelled! Sven Wang
University of Cambridge

Event Details

Research Seminar in Statistics

Title	cancelled ! tba
Speaker, Affiliation	cencelled! Sven Wang , University of Cambridge
Date, Time	27 March 2020, 14:00-14:45
Location	HG G 19.2
Abstract	tba

cancelled ! tbaread_more (CANCELLED)

HG G 19.2

3 April 2020
15:15-16:00

cancelled! Ernst Wit
Università della Svizzera italiana, Lugano

Event Details

Research Seminar in Statistics

Title	cancelled! tba
Speaker, Affiliation	cancelled! Ernst Wit, Università della Svizzera italiana, Lugano
Date, Time	3 April 2020, 15:15-16:00
Location	HG G 19.2
Abstract	tba

cancelled! tbaread_more (CANCELLED)

HG G 19.2

24 April 2020
15:15-16:00

cancelled! Ming Yuan
ETH-ITS und Columbia University

Event Details

Research Seminar in Statistics

Title	cancelld! tba
Speaker, Affiliation	cancelled! Ming Yuan, ETH-ITS und Columbia University
Date, Time	24 April 2020, 15:15-16:00
Location	HG G 19.2

cancelld! tba (CANCELLED)

HG G 19.2

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