On the Distance Between Mean and Geometric Median in High Dimensions
MCML Authors
Mathias Drton
Prof. Dr.
Principal Investigator
Abstract
Mathias Drton
Prof. Dr.
Principal Investigator
Abstract
The geometric median, a notion of center for multivariate distributions, has gained recent attention in robust statistics and machine learning. Although conceptually distinct from the mean (i.e., expectation), we demonstrate that both are very close in high dimensions when the dependence between the distribution components is suitably controlled. Concretely, we find an upper bound on the distance that vanishes with the dimension asymptotically, and derive a rate-matching first order expansion of the geometric median components. Simulations illustrate and confirm our results.
misc
Preprint
Aug. 2025Authors
R. Schwank • M. DrtonLinks
Research Area
BibTeXKey: SD25b