mlsanityData to 14 Oct 2026

Mixed-Curvature Decision Trees and Random Forests

arXiv 2406.05227 ↗First posted 7 Jun 2024cs.LGcited by 0

Not on the map. Why?

Abstract (arXiv)

We extend decision tree and random forest algorithms to product space manifolds: Cartesian products of Euclidean, hyperspherical, and hyperbolic manifolds. Such spaces have extremely expressive geometries capable of representing many arrangements of distances with low metric distortion. To date, all classifiers for product spaces fit a single linear decision boundary, and no regressor has been described. Our method enables a simple, expressive method for classification and regression in product manifolds. We demonstrate the superior accuracy of our tool compared to Euclidean methods operating in the ambient space or the tangent plane of the manifold across a range of constant-curvature and product manifolds. Code for our implementation and experiments is available at https://github.com/pchlenski/embedders.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 28 of its 69 references that are in the map. First posted on arXiv 7 Jun 2024.

Builds on

28 of 69 references.

References · 28

  1. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 684
  2. 2018Hyperbolic Neural Networkscited by 402
  3. 2019Hyperbolic Graph Convolutional Neural Networkscited by 402
  4. 2018Riemannian Adaptive Optimization Methodscited by 194
  5. 2017Cooperative Game Theory Approaches for Network Partitioningcited by 135
  6. 2019Constant Curvature Graph Convolutional Networkscited by 108
  7. 2019Mixed-curvature Variational Autoencoderscited by 86
  8. 2017Neural Embeddings of Graphs in Hyperbolic Spacecited by 58
  9. 2018Large-Margin Classification in Hyperbolic Spacecited by 41
  10. 2020Tree! I am no Tree! I am a Low Dimensional Hyperbolic Embeddingcited by 36
  11. 2021A Self-supervised Mixed-curvature Graph Neural Networkcited by 33
  12. 2022Heterogeneous manifolds for curvature-aware graph embeddingcited by 23
16 more
  1. 2022Latent Graph Inference using Product Manifoldscited by 23
  2. 2023Neural Latent Geometry Search: Product Manifold Inference via Gromov-Hausdorff-Informed Bayesian Optimizationcited by 18
  3. 2020Product Manifold Learningcited by 16
  4. 2023Curve Your Attention: Mixed-Curvature Transformers for Graph Representation Learningcited by 15
  5. 2019Fr'echet random forests for metric space valued regression with non euclidean predictorscited by 13
  6. 2018Is rotation forest the best classifier for problems with continuous features?cited by 11
  7. 2021Linear Classifiers in Product Space Formscited by 11
  8. 2023Hyperbolic Random Forestscited by 9
  9. 2023Fast hyperboloid decision tree algorithmscited by 7
  10. 2017Random Forest regression for manifold-valued responsescited by 6
  11. 2023Neural Snowflakes: Universal Latent Graph Inference via Trainable Latent Geometriescited by 6
  12. 2023Principal Component Analysis in Space Formscited by 5
  13. 2019Riemannian optimization on the simplex of positive definite matricescited by 4
  14. 2023Improving Heterogeneous Graph Learning with Weighted Mixed-Curvature Product Manifoldcited by 4
  15. 2024Product Manifold Representations for Learning on Biological Pathwayscited by 4
  16. 2019Manifold Oblique Random Forests: Towards Closing the Gap on Convolutional Deep Networkscited by 3

Built on by

Not cited yet.