An Efficient and Continuous Voronoi Density Estimator
Abstract
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.
Cite
Text
Marchetti et al. "An Efficient and Continuous Voronoi Density Estimator." Artificial Intelligence and Statistics, 2023.Markdown
[Marchetti et al. "An Efficient and Continuous Voronoi Density Estimator." Artificial Intelligence and Statistics, 2023.](https://mlanthology.org/aistats/2023/marchetti2023aistats-efficient/)BibTeX
@inproceedings{marchetti2023aistats-efficient,
title = {{An Efficient and Continuous Voronoi Density Estimator}},
author = {Marchetti, Giovanni Luca and Polianskii, Vladislav and Varava, Anastasiia and Pokorny, Florian T. and Kragic, Danica},
booktitle = {Artificial Intelligence and Statistics},
year = {2023},
pages = {4732-4744},
volume = {206},
url = {https://mlanthology.org/aistats/2023/marchetti2023aistats-efficient/}
}