An Efficient and Continuous Voronoi Density Estimator
Giovanni Luca Marchetti, Vladislav Polianskii, Anastasiia Varava, Florian T. Pokorny, Danica Kragic
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.
BibTeX
@InProceedings{pmlr-v206-marchetti23a,
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 = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics},
pages = {4732--4744},
year = {2023},
editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem},
volume = {206},
series = {Proceedings of Machine Learning Research},
month = {25--27 Apr},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v206/marchetti23a/marchetti23a.pdf},
url = {https://proceedings.mlr.press/v206/marchetti23a.html},
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.}
}