<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">We are glad to announce the following talk in the virtual ETH Young Data Science Researcher Seminar Zurich<br class=""><br class="">"Gaussian Spherical Tessellations and Learning Adaptively“ <br class="">by Anna Ma, University of California<br class=""><br class="">Time: Thursday, <b class="">24 February 2021, 15.00 - 16.00</b><br class="">Place: Zoom at <a href="https://ethz.zoom.us/j/62895316484" class="">https://ethz.zoom.us/j/62895316484</a><br class=""><br class=""><br class="">if you like to join, we meet at ETH Zürich, HG G 19.2, to watch the zoom together <br class=""><br class=""><br class="">Abstract: Signed measurements of the form $y_i = sign(\langle a_i, x \rangle)$ for $i \in [M]$ are ubiquitous in large-scale machine learning problems where the overarching task is to recover the unknown, unit norm signal $x \in \mathbb{R}^d$. Oftentimes, measurements can be queried adaptively, for example based on a current approximation of $x$, leading to only a subset of the $M$ measurements being needed. Geometrically, these measurements emit a spherical hyperplane tessellation in $\mathbb{R}^{d}$ where one of the cells in the tessellation contains the unknown vector $x$. Motivated by this problem, in this talk we will present a geometric property related to spherical hyperplane tessellations in $\mathbb{R}^{d}$. Under the assumption that $a_i$ are Gaussian random vectors, we will show that with high probability there exists a subset of the hyperplanes whose cardinality is on the order of $d\log(d)\log(M)$ such that the radius of the cell containing $x$ induced by these hyperplanes is bounded above by, up to constants, $d\log(d)\log(M)/M$. The work presented is joint work with Rayan Saab and Eric Lybrand.<br class="">M. Azadkia, G. Chinot, J. Hörrmann, M. Löffler, A. Taeb, N. Zhivotovskiy<br class=""><br class=""><br class="">Please take note of the mask requirements for joining this lecture. Further details can be found here, https://ethz.ch/services/en/news-and-events/coronavirus.html<br class=""><br class="">Seminar website: https://math.ethz.ch/sfs/news-and-events/young-data-science.html<br class=""><br class="">Young Data Science Researcher Seminar Zurich – Seminar for Statistics | ETH Zurich<br class="">math.ethz.ch</body></html>