Even Faster Hyperbolic Random Forests: A Beltrami-Klein Wrapper Approach

2025-06-04

AI Summary

This work addresses the challenges of decision-tree modeling in hyperbolic space and the difficulty of reusing Euclidean algorithms. To this end, we propose a model-agnostic encapsulation paradigm that reformulates hyperbolic decision trees (hyperDT) as a preprocessing–Euclidean tree training–postprocessing pipeline within the Beltrami–Klein (BK) model. Our method rigorously preserves Euclidean threshold-split semantics, enabling direct reuse of existing implementations such as scikit-learn’s random forests. By introducing Lorentz–BK coordinate transformations and hyperbolic embedding adaptation, it achieves plug-and-play cross-geometric transfer. Experiments on hierarchical data demonstrate significant accuracy gains, accelerated training and inference, and substantially improved code conciseness, maintainability, and extensibility. An open-source implementation is publicly available.

Technology Category

Machine Learning: Kernel MethodsReasoning under Uncertainty: Relational Probabilistic ModelsData Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMsUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Decision trees and models that use them as primitives are workhorses of machine learning in Euclidean spaces. Recent work has further extended these models to the Lorentz model of hyperbolic space by replacing axis-parallel hyperplanes with homogeneous hyperplanes when partitioning the input space. In this paper, we show how the hyperDT algorithm can be elegantly reexpressed in the Beltrami-Klein model of hyperbolic spaces. This preserves the thresholding operation used in Euclidean decision trees, enabling us to further rewrite hyperDT as simple pre- and post-processing steps that form a wrapper around existing tree-based models designed for Euclidean spaces. The wrapper approach unlocks many optimizations already available in Euclidean space models, improving flexibility, speed, and accuracy while offering a simpler, more maintainable, and extensible codebase. Our implementation is available at https://github.com/pchlenski/hyperdt.

Problem

• Extend decision trees to hyperbolic space using Beltrami-Klein model
• Enable Euclidean tree models via pre- and post-processing wrapper
• Improve speed, accuracy, and maintainability of hyperbolic forests

Innovation

• Reformulate hyperDT in Beltrami-Klein model
• Wrapper approach simplifies tree-based models
• Enhances speed, accuracy, and maintainability