AISTATS 2021poster15 citations
A Statistical Perspective on Coreset Density Estimation
Paxton Turner, Jingbo Liu, Philippe Rigollet
Abstract
Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of statistical procedures run on coresets is largely unexplored. In this work, we develop a statistical framework to study coresets and focus on the canonical task of nonparameteric density estimation. Our contributions are twofold. First, we establish the minimax rate of estimation achievable by coreset-based estimators. Second, we show that the practical coreset kernel density estimators are near-minimax optimal over a large class of Holder-smooth densities.
BibTeX
@InProceedings{pmlr-v130-turner21b,
title = { A Statistical Perspective on Coreset Density Estimation },
author = {Turner, Paxton and Liu, Jingbo and Rigollet, Philippe},
booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics},
pages = {2512--2520},
year = {2021},
editor = {Banerjee, Arindam and Fukumizu, Kenji},
volume = {130},
series = {Proceedings of Machine Learning Research},
month = {13--15 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v130/turner21b/turner21b.pdf},
url = {https://proceedings.mlr.press/v130/turner21b.html},
abstract = { Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of statistical procedures run on coresets is largely unexplored. In this work, we develop a statistical framework to study coresets and focus on the canonical task of nonparameteric density estimation. Our contributions are twofold. First, we establish the minimax rate of estimation achievable by coreset-based estimators. Second, we show that the practical coreset kernel density estimators are near-minimax optimal over a large class of Holder-smooth densities. }
}