# Uniform convergence of local Fr'echet regression, with applications to locating extrema and time warping for metric space valued trajectories

arXiv: https://arxiv.org/abs/2006.13548 · HTML: https://mlsanity.com/paper/2006.13548/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2020.

## Built on by (most cited first, 8 of 8)

- [Random Forest Weighted Local Fr'echet Regression with Random Objects](https://mlsanity.com/paper/2202.04912/) (2022)
- [Doubly robust estimation of causal effects for random object outcomes with continuous treatments](https://mlsanity.com/paper/2506.22754/) (2025)
- [DFNN: A Deep Fr'echet Neural Network Framework for Learning Metric-Space-Valued Responses](https://mlsanity.com/paper/2510.17072/) (2025)
- [An Optimal Transport Approach for Network Regression](https://mlsanity.com/paper/2406.12204/) (2024)
- [Geometric Renyi Differential Privacy: Ricci Curvature Characterized by Heat Diffusion Mechanisms](https://mlsanity.com/paper/2604.20761/) (2026)
- [Semi-supervised Fr'echet Regression](https://mlsanity.com/paper/2404.10444/) (2024)
- [Metric space valued Fr'echet regression](https://mlsanity.com/paper/2602.05225/) (2026)
- [Deep Single-Index Fr'echet Regression](https://mlsanity.com/paper/2606.06957/) (2026)

## Abstract (arXiv)

Local Fr'echet regression is a nonparametric regression method for metric space valued responses and Euclidean predictors, which can be utilized to obtain estimates of smooth trajectories taking values in general metric spaces from noisy metric space valued random objects. We derive uniform rates of convergence, which so far have eluded theoretical analysis of this method, for both fixed and random target trajectories, where we utilize tools from empirical processes. These results are shown to be widely applicable in metric space valued data analysis. In addition to simulations, we provide two pertinent examples where these results are important: The consistent estimation of the location of properly defined extrema in metric space valued trajectories, which we illustrate with the problem of locating the age of minimum brain connectivity as obtained from fMRI data; Time warping for metric space valued trajectories, illustrated with yearly age-at-death distributions for different countries.