# A Statistical Perspective on Coreset Density Estimation

arXiv: https://arxiv.org/abs/2011.04907 · HTML: https://mlsanity.com/paper/2011.04907/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2020.

## Built on by (most cited first, 6 of 6)

- [Kernel Thinning](https://mlsanity.com/paper/2105.05842/) (2021)
- [Positively Weighted Kernel Quadrature via Subsampling](https://mlsanity.com/paper/2107.09597/) (2021)
- [PSD Representations for Effective Probability Models](https://mlsanity.com/paper/2106.16116/) (2021)
- [Breaking the Linear Iteration Cost Barrier for Some Well-known Conditional Gradient Methods Using MaxIP Data-structures](https://mlsanity.com/paper/2111.15139/) (2021)
- [Leveraging Importance Weights in Subset Selection](https://mlsanity.com/paper/2301.12052/) (2023)
- [Skeleton Clustering: Dimension-Free Density-based Clustering](https://mlsanity.com/paper/2104.10770/) (2021)

## Abstract (arXiv)

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 H"older-smooth densities.