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Peer-reviewedCC BY 4.0Transactions on Machine Learning Research

CURS: an exact method for sampling on Riemannian manifolds

  • Isabella Costa Maia
  • Marco Congedo
  • Pedro Luiz Coelho Rodrigues
  • Salem Said
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Abstract

The present work introduces curvature-based rejection sampling (CURS). This is a method for sampling from a general class of probability densities defined on Riemannian manifolds. It can be used to sample from any probability density which “depends only on distance". The idea is to combine the statistical principle of rejection sampling with the geometric principle of volume comparison. CURS is an exact sampling method and (assuming the underlying Riemannian manifold satisfies certain technical assumptions) it has a particularly moderate computational cost. The aim of the present work is to show that there are many applications where CURS should be the user’s method of choice for dealing with relatively low-dimensional scenarios.

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Cite

BibTeXRIS
BibTeX
@article{maia2026curs,
  title = {{CURS: an exact method for sampling on Riemannian manifolds}},
  author = {Isabella Costa Maia and Marco Congedo and Pedro Luiz Coelho Rodrigues and Salem Said},
  journal = {Transactions on Machine Learning Research},
  year = {2026},
  month = jun,
  url = {https://hal.science/hal-05332278v4},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - CURS: an exact method for sampling on Riemannian manifolds
AU  - Isabella Costa Maia
AU  - Marco Congedo
AU  - Pedro Luiz Coelho Rodrigues
AU  - Salem Said
PY  - 2026
DA  - 2026/06/11
JO  - Transactions on Machine Learning Research
UR  - https://hal.science/hal-05332278v4
AB  - The present work introduces curvature-based rejection sampling (CURS). This is a method for sampling from a general class of probability densities defined on Riemannian manifolds. It can be used to sample from any probability density which “depends only on distance". The idea is to combine the statistical principle of rejection sampling with the geometric principle of volume comparison. CURS is an exact sampling method and (assuming the underlying Riemannian manifold satisfies certain technical assumptions) it has a particularly moderate computational cost. The aim of the present work is to show that there are many applications where CURS should be the user’s method of choice for dealing with relatively low-dimensional scenarios.
SN  - 2835-8856
ER  -