# Voronoi Density Estimator for High-Dimensional Data: Computation, Compactification and Convergence

arXiv: https://arxiv.org/abs/2206.08051 · HTML: https://mlsanity.com/paper/2206.08051/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2022.

## Built on by (most cited first, 7 of 7)

- [A Bag-of-Prototypes Representation for Dataset-Level Applications](https://mlsanity.com/paper/2303.13251/) (2023)
- [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)
- [Divide et Calibra: Multiclass Local Calibration via Vector Quantization](https://mlsanity.com/paper/2605.21060/) (2026)
- [Density Estimation via Binless Multidimensional Integration](https://mlsanity.com/paper/2407.08094/) (2024)
- [Inference with K-means](https://mlsanity.com/paper/2410.17256/) (2024)
- [A Geometric View of Counterfactual Behavior: Interaction of Boundary Proximity and Local Support](https://mlsanity.com/paper/2606.04209/) (2026)

## Abstract (arXiv)

The Voronoi Density Estimator (VDE) is an established density estimation technique that adapts to the local geometry of data. However, its applicability has been so far limited to problems in two and three dimensions. This is because Voronoi cells rapidly increase in complexity as dimensions grow, making the necessary explicit computations infeasible. We define a variant of the VDE deemed Compactified Voronoi Density Estimator (CVDE), suitable for higher dimensions. We propose computationally efficient algorithms for numerical approximation of the CVDE and formally prove convergence of the estimated density to the original one. We implement and empirically validate the CVDE through a comparison with the Kernel Density Estimator (KDE). Our results indicate that the CVDE outperforms the KDE on sound and image data.