# Fr'echet random forests for metric space valued regression with non euclidean predictors

arXiv: https://arxiv.org/abs/1906.01741 · HTML: https://mlsanity.com/paper/1906.01741/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2019.

## Built on by (most cited first, 13 of 13)

- [Random Forest Weighted Local Fr'echet Regression with Random Objects](https://mlsanity.com/paper/2202.04912/) (2022)
- [Medoid splits for efficient random forests in metric spaces](https://mlsanity.com/paper/2306.17031/) (2023)
- [Errors-in-variables Fr'echet Regression with Low-rank Covariate Approximation](https://mlsanity.com/paper/2305.09282/) (2023)
- [Mixed-curvature decision trees and random forests](https://mlsanity.com/paper/2410.13879/) (2024)
- [Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces](https://mlsanity.com/paper/2507.15741/) (2025)
- [End-to-End Deep Learning for Predicting Metric Space-Valued Outputs](https://mlsanity.com/paper/2509.23544/) (2025)
- [DFNN: A Deep Fr'echet Neural Network Framework for Learning Metric-Space-Valued Responses](https://mlsanity.com/paper/2510.17072/) (2025)
- [Geometric Renyi Differential Privacy: Ricci Curvature Characterized by Heat Diffusion Mechanisms](https://mlsanity.com/paper/2604.20761/) (2026)
- [Mixed-Curvature Decision Trees and Random Forests](https://mlsanity.com/paper/2406.05227/) (2024)
- [Fr'echet Geodesic Boosting](https://mlsanity.com/paper/2509.18013/) (2025)
- [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)
- [Kernel of Partition Paths: A Unified Representation for Tree Ensembles](https://mlsanity.com/paper/2606.18853/) (2026)

## Abstract (arXiv)

Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional data. However, current random forest approaches are not flexible enough to handle heterogeneous data such as curves, images and shapes. In this paper, we introduce Fr'echet trees and Fr'echet random forests, which allow to handle data for which input and output variables take values in general metric spaces. To this end, a new way of splitting the nodes of trees is introduced and the prediction procedures of trees and forests are generalized. Then, random forests out-of-bag error and variable importance score are naturally adapted. A consistency theorem for Fr'echet regressogram predictor using data-driven partitions is given and applied to Fr'echet purely uniformly random trees. The method is studied through several simulation scenarios on heterogeneous data combining longitudinal, image and scalar data. Finally, one real dataset about air quality is used to illustrate the use of the proposed method in practice.