# Medoid splits for efficient random forests in metric spaces

arXiv: https://arxiv.org/abs/2306.17031 · HTML: https://mlsanity.com/paper/2306.17031/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 29 Jun 2023.

## Builds on (most cited first, 9 of 9)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation](https://mlsanity.com/paper/1603.03236/) (2016)
- [Hyperparameters and Tuning Strategies for Random Forest](https://mlsanity.com/paper/1804.03515/) (2018)
- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [Confidence Intervals for Random Forests: The Jackknife and the Infinitesimal Jackknife](https://mlsanity.com/paper/1311.4555/) (2013)
- [Distribution-on-Distribution Regression via Optimal Transport Maps](https://mlsanity.com/paper/2104.09418/) (2021)
- [Fr'echet random forests for metric space valued regression with non euclidean predictors](https://mlsanity.com/paper/1906.01741/) (2019)
- [MABSplit: Faster Forest Training Using Multi-Armed Bandits](https://mlsanity.com/paper/2212.07473/) (2022)

## Built on by (most cited first, 7 of 7)

- [Uncertainty quantification in metric spaces](https://mlsanity.com/paper/2405.05110/) (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)
- [Efficient Decision Trees for Tensor Regressions](https://mlsanity.com/paper/2408.01926/) (2024)
- [Variable Selection Methods for Multivariate, Functional, and Complex Biomedical Data in the AI Age](https://mlsanity.com/paper/2501.06868/) (2025)
- [CellxPert: Inference-Time MCMC Steering of a Multi-Omics Single-Cell Foundation Model for In-Silico Perturbation](https://mlsanity.com/paper/2605.00930/) (2026)
- [Random-Effects Algorithm for Random Objects in Metric Spaces](https://mlsanity.com/paper/2605.02693/) (2026)

## Abstract (arXiv)

This paper revisits an adaptation of the random forest algorithm for Fr'echet regression, addressing the challenge of regression in the context of random objects in metric spaces. Recognizing the limitations of previous approaches, we introduce a new splitting rule that circumvents the computationally expensive operation of Fr'echet means by substituting with a medoid-based approach. We validate this approach by demonstrating its asymptotic equivalence to Fr'echet mean-based procedures and establish the consistency of the associated regression estimator. The paper provides a sound theoretical framework and a more efficient computational approach to Fr'echet regression, broadening its application to non-standard data types and complex use cases.