# Geometric Rates of Convergence for Kernel-based Sampling Algorithms

arXiv: https://arxiv.org/abs/1907.08410 · HTML: https://mlsanity.com/paper/1907.08410/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2019.

## Built on by (most cited first, 2 of 2)

- [Efficient Numerical Integration in Reproducing Kernel Hilbert Spaces via Leverage Scores Sampling](https://mlsanity.com/paper/2311.13548/) (2023)
- [Slithering Through Gaps: Capturing Discrete Isolated Modes via Logistic Bridging](https://mlsanity.com/paper/2604.10821/) (2026)

## Abstract (arXiv)

The rate of convergence of weighted kernel herding (WKH) and sequential Bayesian quadrature (SBQ), two kernel-based sampling algorithms for estimating integrals with respect to some target probability measure, is investigated. Under verifiable conditions on the chosen kernel and target measure, we establish a near-geometric rate of convergence for target measures that are nearly atomic. Furthermore, we show these algorithms perform comparably to the theoretical best possible sampling algorithm under the maximum mean discrepancy. An analysis is also conducted in a distributed setting. Our theoretical developments are supported by empirical observations on simulated data as well as a real world application.