# Random Forest Weighted Local Fr'echet Regression with Random Objects

arXiv: https://arxiv.org/abs/2202.04912 · HTML: https://mlsanity.com/paper/2202.04912/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 49 references that are in the map.
- First posted on arXiv 10 Feb 2022.

## Builds on (most cited first, 13 of 13)

- [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)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [Iterative Random Forests to detect predictive and stable high-order interactions](https://mlsanity.com/paper/1706.08457/) (2017)
- [Local Linear Forests](https://mlsanity.com/paper/1807.11408/) (2018)
- [Asymptotic Distributions and Rates of Convergence for Random Forests via Generalized U-statistics](https://mlsanity.com/paper/1905.10651/) (2019)
- [Fr'echet random forests for metric space valued regression with non euclidean predictors](https://mlsanity.com/paper/1906.01741/) (2019)
- [Functional Models for Time-Varying Random Objects](https://mlsanity.com/paper/1907.10829/) (2019)
- [Analysis of purely random forests bias](https://mlsanity.com/paper/1407.3939/) (2014)
- [Single Index Fr'echet Regression](https://mlsanity.com/paper/2108.05437/) (2021)
- [Uniform convergence of local Fr'echet regression, with applications to locating extrema and time warping for metric space valued trajectories](https://mlsanity.com/paper/2006.13548/) (2020)
- [Consistency of Online Random Forests](https://mlsanity.com/paper/1302.4853/) (2013)

## Built on by (most cited first, 12 of 12)

- [On Conditional Stochastic Interpolation for Generative Nonlinear Sufficient Dimension Reduction](https://mlsanity.com/paper/2512.18971/) (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)
- [Fr'echet Cumulative Covariance Net for Deep Nonlinear Sufficient Dimension Reduction with Random Objects](https://mlsanity.com/paper/2502.15374/) (2025)
- [Fr'echet regression with implicit denoising and multicollinearity reduction](https://mlsanity.com/paper/2412.18247/) (2024)
- [Fr'echet Geodesic Boosting](https://mlsanity.com/paper/2509.18013/) (2025)
- [Toward an Asymptotic Efficiency Theory on Regular Parameter Manifolds](https://mlsanity.com/paper/2510.13703/) (2025)
- [Distributional Random Forests for Complex Survey Designs](https://mlsanity.com/paper/2512.08179/) (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)
- [Interpretable AI with Local Distillation](https://mlsanity.com/paper/2608.23538/) (2026)
- [Marginal Coordinate Test for Fr'echet Regression with Random Objects](https://mlsanity.com/paper/2608.30644/) (2026)

## Abstract (arXiv)

Statistical analysis is increasingly confronted with complex data from metric spaces. Petersen and M"uller (2019) established a general paradigm of Fr'echet regression with complex metric space valued responses and Euclidean predictors. However, the local approach therein involves nonparametric kernel smoothing and suffers from the curse of dimensionality. To address this issue, we in this paper propose a novel random forest weighted local Fr'echet regression paradigm. The main mechanism of our approach relies on a locally adaptive kernel generated by random forests. Our first method uses these weights as the local average to solve the conditional Fr'echet mean, while the second method performs local linear Fr'echet regression, both significantly improving existing Fr'echet regression methods. Based on the theory of infinite order U-processes and infinite order Mmn-estimator, we establish the consistency, rate of convergence, and asymptotic normality for our local constant estimator, which covers the current large sample theory of random forests with Euclidean responses as a special case. Numerical studies show the superiority of our methods with several commonly encountered types of responses such as distribution functions, symmetric positive-definite matrices, and sphere data. The practical merits of our proposals are also demonstrated through the application to New York taxi data and human mortality data.