Date: Friday, 12 December 2025, at 12.30pm (CET)

Dual format: ESSEC Paris La Défense (CNIT), Room TBA
and via Zoom, please click here

In a multivariate space, data depth is a statistical function that measures the centrality of a point with respect to a distribution or a data set. Thanks to desirable properties of robustness and invariance, data depth functions are currently used in a variety of tasks as a generalization of quantiles and ranks to higher dimensions and as an alternative to the distribution function, with Tukey’s halfspace depth being the seminal and yet most studied in the literature. Nevertheless, its applications are impeded by the high complexity of exact algorithms (which is exponential with respect to dimension) and the lack of efficient approximation methods, in particular those delivering corresponding guarantees on the approximated value. In the current work, we propose an algorithm able to compute halfspace depth efficiently and to derive the required statistical guarantees for the obtained depth value. More precisely, we exploit the fact that--once in a proper attraction basin--the value of the halfspace depth can be found as the solution of a quasiconvex optimization problem. We propose an iterative, gradient-based algorithm running over the surface of the unit hypersphere, which allows for the derivation of the corresponding guarantees on the empirical halfspace depth value.This is a joint work with Jérémy Guérin, Yann Issartel and Pavlo Mozharovskyi.

Kind regards,
Jeremy Heng, Olga Klopp, Roberto Reno, Marie Kratz and Riada Djebbar (Singapore Actuarial Society - ERM)