Work

Metric space valued Fréchet regression

Year: 2026

Type: preprint

Abstract: We consider the problem of estimating the Fréchet and conditional Fréchet mean from data taking values in separable metric spaces. Unlike Euclidean spaces, where well-established methods are available, there is no practical estimator that works universally for all metric spaces. Therefore, we introduce a computable estimator for the Fréchet mean based on random quantization techniques and establish its universal consistency across any separable metric spaces. Additionally, we propose another estimator for the conditional Fréchet mean, leveraging data-driven partitioning and quantization, and demonstrate its universal consistency when the output space is any Banach space.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2602.05225

Authors: Györfi, László, Humbert, Pierre, Bars, Batiste Le

Institutions: Budapest University of Technology and Economics, Centre National de la Recherche Scientifique, Université Paris-Saclay, Laboratoire de Mathématiques et Modélisation d'Évry

Language: English

Topic: Advanced Statistical Methods and Models

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Sorbonne Université

OpenAlex ID: W7128000911

Cites:

Cited by:

Related to: