Asymptotic topological data analysis for point processes

Abstract: Topological Data Analysis has in the past year attracted more attention in various fields such as in material sciences to study the properties of porous material or in statistics to study the asymptotic properties of random objects. However, topological data analysis still appears hard to grasp for many statisticians.

This talk intends to be an introduction to topological data analysis and therefore does not require any background in the field. We will present an overview of the different approaches in topological data analysis and will focus on the persistent homology approach. We will present the framework of this approach and its main mathematical objects. Finally, we come back to the land of Probability and will present a central limit theorem for the so-called Betti numbers obtained from stationary point processes, non-necessarily Poisson.

machine learningprobabilitystatistics theory

Audience: researchers in the discipline

Gothenburg statistics seminar

Series comments: Gothenburg statistics seminar is open to the interested public, everybody is welcome. It usually takes place in MVL14 (http://maps.chalmers.se/#05137ad7-4d34-45e2-9d14-7f970517e2b60, see specific talk).