[Statlist] Reminder: ETH Young Data Science Researcher Seminar Zurich, Virtual Seminar by Nabarun Deb, Columbia University

[Maurer Letizia]

Dear all

We are glad to announce the following talk in the virtual ETH Young Data Science Researcher Seminar Zurich

"Measuring Association on Topological Spaces Using Kernels and Geometric Graphs"  
by Nabarun Deb, Columbia University


Time: Friday, 13 November 2020, 15:00-​16:00
Place: Zoom at https://ethz.zoom.us/j/92367940258

Abstract: In this work, we propose a class of simple, nonparametric, yet interpretable measures of association between two random variables X and Y taking values in general topological spaces. These nonparametric measures — defined using the theory of reproducing kernel Hilbert spaces — capture the strength of dependence between X and Y and have the property that they are 0 if and only if the variables are independent and 1 if and only if one variable is a measurable function of the other. Further, these population measures can be consistently estimated using the general framework of geometric graphs which include k-​nearest neighbor graphs and minimum spanning trees. Moreover, a sub-​class of these estimators are also shown to adapt to the intrinsic dimensionality of the underlying distribution. Some of these empirical measures can also be computed in near-​linear time. If X and Y are independent, these empirical measures (properly normalized) have a standard normal limiting distribution and hence, can be readily used to test for independence. In fact, as far as we are aware, these are the only procedures that possess all the above mentioned desirable properties. The correlation coefficient proposed in Dette et al. [31], Chatterjee [22], and Azadkia and Chatterjee [7] can be seen as a special case of this general class of measures. If time permits, I will also describe how the same ideas can be effectively used to measure the strength of conditional dependence. The talk is based on this paper https://arxiv.org/abs/2010.01768.

Best wishes,

M. Azadkia, Y. Chen, M. Löffler, A. Taeb

Seminar website: https://math.ethz.ch/sfs/news-and-events/young-data-science.html