# An Efficient and Continuous Voronoi Density Estimator

arXiv: https://arxiv.org/abs/2210.03964 · HTML: https://mlsanity.com/paper/2210.03964/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2022.

## Built on by (most cited first, 3 of 3)

- [Winner-takes-all learners are geometry-aware conditional density estimators](https://mlsanity.com/paper/2406.04706/) (2024)
- [Geometry-Aware Probabilistic Circuits via Voronoi Tessellations](https://mlsanity.com/paper/2603.11946/) (2026)
- [Density Estimation via Binless Multidimensional Integration](https://mlsanity.com/paper/2407.08094/) (2024)

## Abstract (arXiv)

We introduce a non-parametric density estimator deemed Radial Voronoi Density Estimator (RVDE). RVDE is grounded in the geometry of Voronoi tessellations and as such benefits from local geometric adaptiveness and broad convergence properties. Due to its radial definition RVDE is continuous and computable in linear time with respect to the dataset size. This amends for the main shortcomings of previously studied VDEs, which are highly discontinuous and computationally expensive. We provide a theoretical study of the modes of RVDE as well as an empirical investigation of its performance on high-dimensional data. Results show that RVDE outperforms other non-parametric density estimators, including recently introduced VDEs.