mlsanityData to 14 Oct 2026

Stationary MMD Points

arXiv 2505.20754 ↗First posted 27 May 2025stat.ML cs.LGcited by 2

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Abstract (arXiv)

Approximation of a target probability distribution using a finite set of points is a problem of fundamental importance in numerical integration. Several authors have proposed to select points by minimising a maximum mean discrepancy (MMD), but the non-convexity of this objective typically precludes global minimisation. Instead, we consider the concept of stationary points of the MMD which, in contrast to points globally minimising the MMD, can be accurately computed. Our main contributions are two-fold and theoretical in nature. We first prove the (perhaps surprising) result that, for integrands in the associated reproducing kernel Hilbert space, the numerical integration error of stationary MMD points vanishes faster than the MMD. Motivated by this super-convergence property, we consider MMD gradient flows as a practical strategy for computing stationary points of the MMD. We then prove that MMD gradient flow can indeed compute stationary MMD points, based on a refined convergence analysis that establishes a novel non-asymptotic finite-particle error bound.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 44 of its 95 references that are in the map. First posted on arXiv 27 May 2025.

Builds on

44 of 95 references.

References · 44

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32 more
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2026Thinned Mean Field Langevin Dynamicscited by 1
  2. 2025BayesSum: Bayesian Quadrature in Discrete Spacescited by 0