# Generalized Kernel Thinning

arXiv: https://arxiv.org/abs/2110.01593 · HTML: https://mlsanity.com/paper/2110.01593/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 70 references that are in the map.
- First posted on arXiv 4 Oct 2021.

## Builds on (most cited first, 17 of 17)

- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [Control functionals for Monte Carlo integration](https://mlsanity.com/paper/1410.2392/) (2014)
- [Kernel Thinning](https://mlsanity.com/paper/2105.05842/) (2021)
- [Stein Points](https://mlsanity.com/paper/1803.10161/) (2018)
- [Support points](https://mlsanity.com/paper/1609.01811/) (2016)
- [Metrizing Weak Convergence with Maximum Mean Discrepancies](https://mlsanity.com/paper/2006.09268/) (2020)
- [Near-Optimal Coresets of Kernel Density Estimates](https://mlsanity.com/paper/1802.01751/) (2018)
- [Discrepancy, Coresets, and Sketches in Machine Learning](https://mlsanity.com/paper/1906.04845/) (2019)
- [Stein Point Markov Chain Monte Carlo](https://mlsanity.com/paper/1905.03673/) (2019)
- [Optimal Thinning of MCMC Output](https://mlsanity.com/paper/2005.03952/) (2020)
- [Finding Global Minima via Kernel Approximations](https://mlsanity.com/paper/2012.11978/) (2020)
- [Sequential Kernel Herding: Frank-Wolfe Optimization for Particle Filtering](https://mlsanity.com/paper/1501.02056/) (2015)
- [Statistically efficient thinning of a Markov chain sampler](https://mlsanity.com/paper/1510.07727/) (2015)
- [The power of online thinning in reducing discrepancy](https://mlsanity.com/paper/1608.02895/) (2016)

## Built on by (most cited first, 29 of 29)

- [Distribution Compression in Near-linear Time](https://mlsanity.com/paper/2111.07941/) (2021)
- [Sampling-based Nystr"om Approximation and Kernel Quadrature](https://mlsanity.com/paper/2301.09517/) (2023)
- [Compress Then Test: Powerful Kernel Testing in Near-linear Time](https://mlsanity.com/paper/2301.05974/) (2023)
- [Counterfactual inference in sequential experiments](https://mlsanity.com/paper/2202.06891/) (2022)
- [Weighted quantization using MMD: From mean field to mean shift via gradient flows](https://mlsanity.com/paper/2502.10600/) (2025)
- [Kernel quadrature with randomly pivoted Cholesky](https://mlsanity.com/paper/2306.03955/) (2023)
- [Efficient Numerical Integration in Reproducing Kernel Hilbert Spaces via Leverage Scores Sampling](https://mlsanity.com/paper/2311.13548/) (2023)
- [Online Kernel CUSUM for Change-Point Detection](https://mlsanity.com/paper/2211.15070/) (2022)
- [Coordinating Distributed Example Orders for Provably Accelerated Training](https://mlsanity.com/paper/2302.00845/) (2023)
- [Low-Rank Thinning](https://mlsanity.com/paper/2502.12063/) (2025)
- [Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approach](https://mlsanity.com/paper/2306.05843/) (2023)
- [WildCat: Near-Linear Attention in Theory and Practice](https://mlsanity.com/paper/2602.10056/) (2026)
- [Submodular Framework for Structured-Sparse Optimal Transport](https://mlsanity.com/paper/2406.04914/) (2024)
- [Bayesian Reinforcement Learning with Limited Cognitive Load](https://mlsanity.com/paper/2305.03263/) (2023)
- [When can Regression-Adjusted Control Variates Help? Rare Events, Sobolev Embedding and Minimax Optimality](https://mlsanity.com/paper/2305.16527/) (2023)
- [Efficient and Accurate Explanation Estimation with Distribution Compression](https://mlsanity.com/paper/2406.18334/) (2024)
- [A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Lifting](https://mlsanity.com/paper/2404.12219/) (2024)
- [Supervised Kernel Thinning](https://mlsanity.com/paper/2410.13749/) (2024)
- [Learning Counterfactual Distributions via Kernel Nearest Neighbors](https://mlsanity.com/paper/2410.13381/) (2024)
- [Stationary MMD Points](https://mlsanity.com/paper/2505.20754/) (2025)
- [Policy Gradient with Kernel Quadrature](https://mlsanity.com/paper/2310.14768/) (2023)
- [Monte Carlo with kernel-based Gibbs measures: Guarantees for probabilistic herding](https://mlsanity.com/paper/2402.11736/) (2024)
- [Geometric Median Matching for Robust k-Subset Selection from Noisy Data](https://mlsanity.com/paper/2504.00564/) (2025)
- [Thinned Mean Field Langevin Dynamics](https://mlsanity.com/paper/2605.28589/) (2026)
- [Quenched large deviations for Monte Carlo integration with Coulomb gases](https://mlsanity.com/paper/2508.01392/) (2025)
- [Bilateral Distribution Compression: Reducing Both Data Size and Dimensionality](https://mlsanity.com/paper/2509.17543/) (2025)
- [Convex-Geometric Error Bounds for Positive-Weight Kernel Quadrature](https://mlsanity.com/paper/2605.05705/) (2026)
- [Express Language Modeling](https://mlsanity.com/paper/2606.10944/) (2026)
- [Revisiting Thinning Methods for Kernel Learning Problems](https://mlsanity.com/paper/2609.07432/) (2026)

## Abstract (arXiv)

The kernel thinning (KT) algorithm of Dwivedi and Mackey (2021) compresses a probability distribution more effectively than independent sampling by targeting a reproducing kernel Hilbert space (RKHS) and leveraging a less smooth square-root kernel. Here we provide four improvements. First, we show that KT applied directly to the target RKHS yields tighter, dimension-free guarantees for any kernel, any distribution, and any fixed function in the RKHS. Second, we show that, for analytic kernels like Gaussian, inverse multiquadric, and sinc, target KT admits maximum mean discrepancy (MMD) guarantees comparable to or better than those of square-root KT without making explicit use of a square-root kernel. Third, we prove that KT with a fractional power kernel yields better-than-Monte-Carlo MMD guarantees for non-smooth kernels, like Laplace and Mat'ern, that do not have square-roots. Fourth, we establish that KT applied to a sum of the target and power kernels (a procedure we call KT+) simultaneously inherits the improved MMD guarantees of power KT and the tighter individual function guarantees of target KT. In our experiments with target KT and KT+, we witness significant improvements in integration error even in 100 dimensions and when compressing challenging differential equation posteriors.