# Optimal quantisation of probability measures using maximum mean discrepancy

arXiv: https://arxiv.org/abs/2010.07064 · HTML: https://mlsanity.com/paper/2010.07064/

## Key facts

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

## Built on by (most cited first, 14 of 14)

- [Weighted quantization using MMD: From mean field to mean shift via gradient flows](https://mlsanity.com/paper/2502.10600/) (2025)
- [Performance analysis of greedy algorithms for minimising a Maximum Mean Discrepancy](https://mlsanity.com/paper/2101.07564/) (2021)
- [Sobolev Spaces, Kernels and Discrepancies over Hyperspheres](https://mlsanity.com/paper/2211.09196/) (2022)
- [Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approach](https://mlsanity.com/paper/2306.05843/) (2023)
- [Online, Informative MCMC Thinning with Kernelized Stein Discrepancy](https://mlsanity.com/paper/2201.07130/) (2022)
- [Benchmarking Bayesian neural networks and evaluation metrics for regression tasks](https://mlsanity.com/paper/2206.06779/) (2022)
- [A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Lifting](https://mlsanity.com/paper/2404.12219/) (2024)
- [Sparse solutions of the kernel herding algorithm by improved gradient approximation](https://mlsanity.com/paper/2105.07900/) (2021)
- [Stationary MMD Points](https://mlsanity.com/paper/2505.20754/) (2025)
- [Bayes Hilbert Spaces for Posterior Approximation](https://mlsanity.com/paper/2304.09053/) (2023)
- [Thinned Mean Field Langevin Dynamics](https://mlsanity.com/paper/2605.28589/) (2026)
- [Scalable Monte Carlo for Bayesian Learning](https://mlsanity.com/paper/2407.12751/) (2024)
- [Multi-output Gaussian process prediction of physical fields under linear equality constraints](https://mlsanity.com/paper/2608.25709/) (2026)
- [On the Optimisation Landscape of Overparameterised Weighted MMD](https://mlsanity.com/paper/2610.19861/) (2026)

## Abstract (arXiv)

Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that greedily minimise MMD over a discrete candidate set. We propose a novel non-myopic algorithm and, in order to both improve statistical efficiency and reduce computational cost, we investigate a variant that applies this technique to a mini-batch of the candidate set at each iteration. When the candidate points are sampled from the target, the consistency of these new algorithm - and their mini-batch variants - is established. We demonstrate the algorithms on a range of important computational problems, including optimisation of nodes in Bayesian cubature and the thinning of Markov chain output.