Antonio Cuevas

Title

On the interplay between Statistics and Geometry: A brief overview and some directions for future research

Abstract

The use of geometrically inspired tools has a long tradition in statistics. In this talk I focus on a specific instance of these geometric connections, commonly referred to as “set estimation theory,” which deals with the problem of estimating a closed set S (or certain subsets or functionals of S) from a sample of points whose distribution is related to S. After briefly reviewing the current state of the art, I will outline some directions for future research, with particular emphasis on those connected to the emerging field of manifold learning.

Keywords

• Set estimation
• Manifold learning
• Manifold hypothesis