# An optimal transport approach for selecting a representative subsample with application in efficient kernel density estimation

arXiv: https://arxiv.org/abs/2206.01182 · HTML: https://mlsanity.com/paper/2206.01182/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 98 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 19 of 19)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Regularized Discrete Optimal Transport](https://mlsanity.com/paper/1307.5551/) (2013)
- [On Markov chain Monte Carlo methods for tall data](https://mlsanity.com/paper/1505.02827/) (2015)
- [A Statistical Perspective on Algorithmic Leveraging](https://mlsanity.com/paper/1306.5362/) (2013)
- [Support points](https://mlsanity.com/paper/1609.01811/) (2016)
- [Optimal Subsampling for Large Sample Logistic Regression](https://mlsanity.com/paper/1702.01166/) (2017)
- [Speeding Up MCMC by Efficient Data Subsampling](https://mlsanity.com/paper/1404.4178/) (2014)
- [Large-scale optimal transport map estimation using projection pursuit](https://mlsanity.com/paper/2106.05838/) (2021)
- [Optimal Distributed Subsampling for Maximum Quasi-Likelihood Estimators with Massive Data](https://mlsanity.com/paper/2005.10435/) (2020)
- [Optimal Subsampling Algorithms for Big Data Regressions](https://mlsanity.com/paper/1806.06761/) (2018)
- [Asymptotic Analysis of Sampling Estimators for Randomized Numerical Linear Algebra Algorithms](https://mlsanity.com/paper/2002.10526/) (2020)
- [Sufficient dimension reduction for classification using principal optimal transport direction](https://mlsanity.com/paper/2010.09921/) (2020)
- [A Review on Modern Computational Optimal Transport Methods with Applications in Biomedical Research](https://mlsanity.com/paper/2008.02995/) (2020)
- [More efficient approximation of smoothing splines via space-filling basis selection](https://mlsanity.com/paper/2003.10609/) (2020)
- [Modern Subsampling Methods for Large-Scale Least Squares Regression](https://mlsanity.com/paper/2105.01552/) (2021)
- [Smoothing splines approximation using Hilbert curve basis selection](https://mlsanity.com/paper/2109.11727/) (2021)
- [Visualization of Big Spatial Data using Coresets for Kernel Density Estimates](https://mlsanity.com/paper/1709.04453/) (2017)

## Built on by (most cited first, 4 of 4)

- [Enhancing Semi-Supervised Learning via Representative and Diverse Sample Selection](https://mlsanity.com/paper/2409.11653/) (2024)
- [A model-free subdata selection method for classification](https://mlsanity.com/paper/2404.19127/) (2024)
- [Core-elements Subsampling for Alternating Least Squares](https://mlsanity.com/paper/2509.18024/) (2025)
- [Knowledge Cascade: Reverse Knowledge Distillation on Nonparametric Multivariate Functional Estimation](https://mlsanity.com/paper/2606.25927/) (2026)

## Abstract (arXiv)

Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of model-based methods, in this paper, we study model-free subsampling methods, which aim to identify a subsample that is not confined by model assumptions. Existing model-free subsampling methods are usually built upon clustering techniques or kernel tricks. Most of these methods suffer from either a large computational burden or a theoretical weakness. In particular, the theoretical weakness is that the empirical distribution of the selected subsample may not necessarily converge to the population distribution. Such computational and theoretical limitations hinder the broad applicability of model-free subsampling methods in practice. We propose a novel model-free subsampling method by utilizing optimal transport techniques. Moreover, we develop an efficient subsampling algorithm that is adaptive to the unknown probability density function. Theoretically, we show the selected subsample can be used for efficient density estimation by deriving the convergence rate for the proposed subsample kernel density estimator. We also provide the optimal bandwidth for the proposed estimator. Numerical studies on synthetic and real-world datasets demonstrate the performance of the proposed method is superior.