SPEAKER: Diego Bolón Rodríguez (ULB)
TITLE: A review on highest density region estimation
ABSTRACT: Highest density regions (HDRs in short) are sets where the density function of the data exceeds a given (and usually high) threshold. Estimating the HDRs of a population from a data sample is a useful tool for data visualization, cluster analysis, and outlier detection. Due to its practical utility, HDR estimation for Euclidean data has been widely considered in the literature. However, HDR estimation in other contexts has only been addressed very recently. In this talk, we introduce the different techniques developed for HDR estimation in the Euclidean context. This introduction allows us to highlight the particular issues of this specific problem, such as how to measure consistency in this context. Then, we explore recent efforts to extend these techniques for populations supported on a manifold, including a novel approach that combines a density function estimator with some a priori geometric information.