[Statlist] Monday, April 10, 2017 with Shahar Mendelson The Australian National University, Canberra, Australia and The Department of Mathematics, Technion, I.I.T, Haifa, Israel

[Maurer Letizia]

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ETH and University of Zurich

Organisers:

Proff. P. Bühlmann - L. Held - T. Hothorn - M. Maathuis -
N. Meinshausen - S. van de Geer - M. Wolf
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We are glad to announce the following talk:

Monday, April 10, 2017 at 15.15h  ETH Zurich HG G 19.241
with Shahar Mendelson (The Australian National University, Canberra, Australia and The Department of Mathematics, Technion, I.I.T, Haifa, Israel)
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Title:

The small-ball method and the structure of random coordinate projections <https://www.math.ethz.ch/sfs/news-and-events/research-seminar.html?s=fs17#e_9890>

Abstract:

We study the geometry of the natural function class extension of a random projection of a subset of $R^d$: for a class of functions $F$ defined on the probability space $(\Omega,\mu)$ and an iid sample X_1,...,X_N with each of the $X_i$'s distributed according to $\mu$, the corresponding coordinate projection of $F$ is the set $\{ (f(X_1),....,f(X_N)) : f \in F\} \subset R^N$. We explain how structural information on such random sets can be derived and then used to address various questions in high dimensional statistics (e.g. regression problems), high dimensional probability (e.g., the extremal singular values of certain random matrices) and high dimensional geometry (e.g., Dvoretzky type theorems). Our focus is on results that are (almost) universally true, with minimal assumptions on the class $F$; these results are established using the recently introduced small-ball method.


This abstract is also to be found under the following link: http://stat.ethz.ch/events/research_seminar

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