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

TL;DR

This paper introduces a wrapper approach for hyperbolic decision trees using the Beltrami-Klein model, enhancing speed, flexibility, and accuracy by leveraging Euclidean decision tree techniques.

Contribution

It reexpresses hyperbolic decision trees within the Beltrami-Klein model, enabling the use of existing Euclidean tree optimizations as a wrapper for improved performance.

Findings

Enhanced speed and accuracy of hyperbolic decision trees.

Simplified implementation with a maintainable codebase.

Leveraged Euclidean optimizations for hyperbolic models.

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.