# Optimizing Kernel Discrepancies via Subset Selection

arXiv: https://arxiv.org/abs/2511.02706 · HTML: https://mlsanity.com/paper/2511.02706/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 49 references that are in the map.
- First posted on arXiv 4 Nov 2025.

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

- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [Minimum Stein Discrepancy Estimators](https://mlsanity.com/paper/1906.08283/) (2019)
- [Kernel Stein Discrepancy Descent](https://mlsanity.com/paper/2105.09994/) (2021)
- [Stein Points](https://mlsanity.com/paper/1803.10161/) (2018)
- [Optimal Thinning of MCMC Output](https://mlsanity.com/paper/2005.03952/) (2020)
- [Kernel Stein Discrepancy thinning: a theoretical perspective of pathologies and a practical fix with regularization](https://mlsanity.com/paper/2301.13528/) (2023)
- [Message-Passing Monte Carlo: Generating low-discrepancy point sets via Graph Neural Networks](https://mlsanity.com/paper/2405.15059/) (2024)
- [Fully Parallel Hyperparameter Search: Reshaped Space-Filling](https://mlsanity.com/paper/1910.08406/) (2019)
- [Heuristic Approaches to Obtain Low-Discrepancy Point Sets via Subset Selection](https://mlsanity.com/paper/2306.15276/) (2023)
- [Improving Efficiency of Sampling-based Motion Planning via Message-Passing Monte Carlo](https://mlsanity.com/paper/2410.03909/) (2024)
- [Star Discrepancy Subset Selection: Problem Formulation and Efficient Approaches for Low Dimensions](https://mlsanity.com/paper/2101.07881/) (2021)
- [On the optimization of discrepancy measures](https://mlsanity.com/paper/2508.04926/) (2025)
- [Outperforming the Best 1D Low-Discrepancy Constructions with a Greedy Algorithm](https://mlsanity.com/paper/2406.18132/) (2024)
- [Sampling in CMA-ES: Low Numbers of Low Discrepancy Points](https://mlsanity.com/paper/2409.15941/) (2024)
- [Neural Low-Discrepancy Sequences](https://mlsanity.com/paper/2510.03745/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Bayesian Approach to Low-Discrepancy Subset Selection](https://mlsanity.com/paper/2602.14607/) (2026)

## Abstract (arXiv)

Kernel discrepancies are a powerful tool for analyzing worst-case errors in quasi-Monte Carlo (QMC) methods. Building on recent advances in optimizing such discrepancy measures, we extend the subset selection problem to the setting of kernel discrepancies, selecting an m-element subset from a large population of size n gg m. We introduce a novel subset selection algorithm applicable to general kernel discrepancies to efficiently generate low-discrepancy samples from both the uniform distribution on the unit hypercube, the traditional setting of classical QMC, and from more general distributions F with known density functions by employing the kernel Stein discrepancy. We also explore the relationship between the classical L2 star discrepancy and its L_∞ counterpart.