Mixed-curvature decision trees and random forests

Philippe Chlenski, Quentin Chu, Raiyan R. Khan, Kaizhu Du, Antonio Khalil Moretti, Itsik Pe’Er
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:10469-10498, 2025.

Abstract

Decision trees (DTs) and their random forest (RF) extensions are workhorses of classification and regression in Euclidean spaces. However, algorithms for learning in non-Euclidean spaces are still limited. We extend DT and RF algorithms to product manifolds: Cartesian products of several hyperbolic, hyperspherical, or Euclidean components. Such manifolds handle heterogeneous curvature while still factorizing neatly into simpler components, making them compelling embedding spaces for complex datasets. Our novel angular reformulation respects manifold geometry while preserving the algorithmic properties that make decision trees effective. In the special cases of single-component manifolds, our method simplifies to its Euclidean or hyperbolic counterparts, or introduces hyperspherical DT algorithms, depending on the curvature. In benchmarks on a diverse suite of 57 classification, regression, and link prediction tasks, our product RFs ranked first on 29 tasks and came in the top 2 for 41. This highlights the value of product RFs as straightforward yet powerful new tools for data analysis in product manifolds. Code for our method is available at https://github.com/pchlenski/manify.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-chlenski25a, title = {Mixed-curvature decision trees and random forests}, author = {Chlenski, Philippe and Chu, Quentin and Khan, Raiyan R. and Du, Kaizhu and Moretti, Antonio Khalil and Pe'Er, Itsik}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {10469--10498}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/chlenski25a/chlenski25a.pdf}, url = {https://proceedings.mlr.press/v267/chlenski25a.html}, abstract = {Decision trees (DTs) and their random forest (RF) extensions are workhorses of classification and regression in Euclidean spaces. However, algorithms for learning in non-Euclidean spaces are still limited. We extend DT and RF algorithms to product manifolds: Cartesian products of several hyperbolic, hyperspherical, or Euclidean components. Such manifolds handle heterogeneous curvature while still factorizing neatly into simpler components, making them compelling embedding spaces for complex datasets. Our novel angular reformulation respects manifold geometry while preserving the algorithmic properties that make decision trees effective. In the special cases of single-component manifolds, our method simplifies to its Euclidean or hyperbolic counterparts, or introduces hyperspherical DT algorithms, depending on the curvature. In benchmarks on a diverse suite of 57 classification, regression, and link prediction tasks, our product RFs ranked first on 29 tasks and came in the top 2 for 41. This highlights the value of product RFs as straightforward yet powerful new tools for data analysis in product manifolds. Code for our method is available at https://github.com/pchlenski/manify.} }
Endnote
%0 Conference Paper %T Mixed-curvature decision trees and random forests %A Philippe Chlenski %A Quentin Chu %A Raiyan R. Khan %A Kaizhu Du %A Antonio Khalil Moretti %A Itsik Pe’Er %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-chlenski25a %I PMLR %P 10469--10498 %U https://proceedings.mlr.press/v267/chlenski25a.html %V 267 %X Decision trees (DTs) and their random forest (RF) extensions are workhorses of classification and regression in Euclidean spaces. However, algorithms for learning in non-Euclidean spaces are still limited. We extend DT and RF algorithms to product manifolds: Cartesian products of several hyperbolic, hyperspherical, or Euclidean components. Such manifolds handle heterogeneous curvature while still factorizing neatly into simpler components, making them compelling embedding spaces for complex datasets. Our novel angular reformulation respects manifold geometry while preserving the algorithmic properties that make decision trees effective. In the special cases of single-component manifolds, our method simplifies to its Euclidean or hyperbolic counterparts, or introduces hyperspherical DT algorithms, depending on the curvature. In benchmarks on a diverse suite of 57 classification, regression, and link prediction tasks, our product RFs ranked first on 29 tasks and came in the top 2 for 41. This highlights the value of product RFs as straightforward yet powerful new tools for data analysis in product manifolds. Code for our method is available at https://github.com/pchlenski/manify.
APA
Chlenski, P., Chu, Q., Khan, R.R., Du, K., Moretti, A.K. & Pe’Er, I.. (2025). Mixed-curvature decision trees and random forests. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:10469-10498 Available from https://proceedings.mlr.press/v267/chlenski25a.html.

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