# Stein Points

arXiv: https://arxiv.org/abs/1803.10161 · HTML: https://mlsanity.com/paper/1803.10161/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2018.

## Built on by (most cited first, 30 of 43)

- [Kernel Stein Discrepancy Descent](https://mlsanity.com/paper/2105.09994/) (2021)
- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [Kernel Thinning](https://mlsanity.com/paper/2105.05842/) (2021)
- [Generalized Kernel Thinning](https://mlsanity.com/paper/2110.01593/) (2021)
- [A Finite-Particle Convergence Rate for Stein Variational Gradient Descent](https://mlsanity.com/paper/2211.09721/) (2022)
- [Sampling with Mirrored Stein Operators](https://mlsanity.com/paper/2106.12506/) (2021)
- [Generalized Coverage for More Robust Low-Budget Active Learning](https://mlsanity.com/paper/2407.12212/) (2024)
- [Targeted Separation and Convergence with Kernel Discrepancies](https://mlsanity.com/paper/2209.12835/) (2022)
- [Controlling Moments with Kernel Stein Discrepancies](https://mlsanity.com/paper/2211.05408/) (2022)
- [Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference](https://mlsanity.com/paper/2301.11674/) (2023)
- [Weighted quantization using MMD: From mean field to mean shift via gradient flows](https://mlsanity.com/paper/2502.10600/) (2025)
- [Kernel Stein Discrepancy thinning: a theoretical perspective of pathologies and a practical fix with regularization](https://mlsanity.com/paper/2301.13528/) (2023)
- [GAD-PVI: A General Accelerated Dynamic-Weight Particle-Based Variational Inference Framework](https://mlsanity.com/paper/2312.16429/) (2023)
- [A Dictionary of Closed-Form Kernel Mean Embeddings](https://mlsanity.com/paper/2504.18830/) (2025)
- [Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates](https://mlsanity.com/paper/2301.11294/) (2023)
- [Performance analysis of greedy algorithms for minimising a Maximum Mean Discrepancy](https://mlsanity.com/paper/2101.07564/) (2021)
- [DPVI: A Dynamic-Weight Particle-Based Variational Inference Framework](https://mlsanity.com/paper/2112.00945/) (2021)
- [Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approach](https://mlsanity.com/paper/2306.05843/) (2023)
- [Probabilistic Inference and Learning with Stein's Method](https://mlsanity.com/paper/2603.07467/) (2026)
- [Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit](https://mlsanity.com/paper/2106.12105/) (2021)
- [Primal and Dual Analysis of Entropic Fictitious Play for Finite-sum Problems](https://mlsanity.com/paper/2303.02957/) (2023)
- [When can Regression-Adjusted Control Variates Help? Rare Events, Sobolev Embedding and Minimax Optimality](https://mlsanity.com/paper/2305.16527/) (2023)
- [Nystr"om Kernel Stein Discrepancy](https://mlsanity.com/paper/2406.08401/) (2024)
- [Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamics](https://mlsanity.com/paper/2411.00214/) (2024)
- [Compressed Monte Carlo with application in particle filtering](https://mlsanity.com/paper/2107.08459/) (2021)
- [A Deterministic Sampling Method via Maximum Mean Discrepancy Flow with Adaptive Kernel](https://mlsanity.com/paper/2111.10722/) (2021)
- [The Minimax Lower Bound of Kernel Stein Discrepancy Estimation](https://mlsanity.com/paper/2510.15058/) (2025)
- [Minimax Estimation of Kernel Stein Discrepancy: Trace versus Hilbert-Schmidt Scales](https://mlsanity.com/paper/2607.03367/) (2026)
- [Low Stein Discrepancy via Message-Passing Monte Carlo](https://mlsanity.com/paper/2503.21103/) (2025)
- [To discretize continually: Mean shift interacting particle systems for Bayesian inference](https://mlsanity.com/paper/2605.14142/) (2026)

## Abstract (arXiv)

An important task in computational statistics and machine learning is to approximate a posterior distribution p(x) with an empirical measure supported on a set of representative points xii=1n. This paper focuses on methods where the selection of points is essentially deterministic, with an emphasis on achieving accurate approximation when n is small. To this end, we present `Stein Points'. The idea is to exploit either a greedy or a conditional gradient method to iteratively minimise a kernel Stein discrepancy between the empirical measure and p(x). Our empirical results demonstrate that Stein Points enable accurate approximation of the posterior at modest computational cost. In addition, theoretical results are provided to establish convergence of the method.