# Fr'echet Geodesic Boosting

arXiv: https://arxiv.org/abs/2509.18013 · HTML: https://mlsanity.com/paper/2509.18013/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 68 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 26 of 26)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [Online Gradient Boosting](https://mlsanity.com/paper/1506.04820/) (2015)
- [Network Regression with Graph Laplacians](https://mlsanity.com/paper/2109.02981/) (2021)
- [Fr'echet random forests for metric space valued regression with non euclidean predictors](https://mlsanity.com/paper/1906.01741/) (2019)
- [Random Forest Weighted Local Fr'echet Regression with Random Objects](https://mlsanity.com/paper/2202.04912/) (2022)
- [Causal Inference on Distribution Functions](https://mlsanity.com/paper/2101.01599/) (2021)
- [Distributional data analysis of accelerometer data from the NHANES database using nonparametric survey regression models](https://mlsanity.com/paper/2104.01165/) (2021)
- [Single Index Fr'echet Regression](https://mlsanity.com/paper/2108.05437/) (2021)
- [Wasserstein Regression with Empirical Measures and Density Estimation for Sparse Data](https://mlsanity.com/paper/2308.12540/) (2023)
- [Regression with Distance Matrices](https://mlsanity.com/paper/1303.3750/) (2013)
- [Manifold valued data analysis of samples of networks, with applications in corpus linguistics](https://mlsanity.com/paper/1902.08290/) (2019)
- [Dimension Reduction for Fr'echet Regression](https://mlsanity.com/paper/2110.00467/) (2021)
- [Geodesic Causal Inference](https://mlsanity.com/paper/2406.19604/) (2024)
- [Intrinsic Riemannian Functional Data Analysis](https://mlsanity.com/paper/1812.01831/) (2018)
- [SketchBoost: Fast Gradient Boosted Decision Tree for Multioutput Problems](https://mlsanity.com/paper/2211.12858/) (2022)
- [Fr'echet single index models for object response regression](https://mlsanity.com/paper/2108.06058/) (2021)
- [Errors-in-variables Fr'echet Regression with Low-rank Covariate Approximation](https://mlsanity.com/paper/2305.09282/) (2023)
- [Principal component analysis and the locus of the Frechet mean in the space of phylogenetic trees](https://mlsanity.com/paper/1609.03045/) (2016)
- [Metric Statistics: Exploration and Inference for Random Objects With Distance Profiles](https://mlsanity.com/paper/2202.06117/) (2022)
- [Wasserstein Gradient Boosting: A Framework for Distribution-Valued Supervised Learning](https://mlsanity.com/paper/2405.09536/) (2024)
- [Deep Fr'echet Regression](https://mlsanity.com/paper/2407.21407/) (2024)
- [Boosted nonparametric hazards with time-dependent covariates](https://mlsanity.com/paper/1701.07926/) (2017)
- [Measure Selection for Functional Linear Model](https://mlsanity.com/paper/2509.00583/) (2025)

## Abstract (arXiv)

Gradient boosting has become a cornerstone of machine learning, enabling base learners such as decision trees to achieve exceptional predictive performance. While existing algorithms primarily handle scalar or Euclidean outputs, increasingly prevalent complex-structured data, such as distributions, networks, and manifold-valued outputs, present challenges for traditional methods. Such non-Euclidean data lack algebraic structures such as addition, subtraction, or scalar multiplication required by standard gradient boosting frameworks. To address these challenges, we introduce Fr'echet geodesic boosting (FGBoost), a novel approach tailored for outputs residing in geodesic metric spaces. FGBoost leverages geodesics as proxies for residuals and constructs ensembles in a way that respects the intrinsic geometry of the output space. Through theoretical analysis, extensive simulations, and real-world applications, we demonstrate the strong performance and adaptability of FGBoost, showcasing its potential for modeling complex data.