# A Bayesian Approach to Low-Discrepancy Subset Selection

arXiv: https://arxiv.org/abs/2602.14607 · HTML: https://mlsanity.com/paper/2602.14607/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 31 references that are in the map.
- First posted on arXiv 16 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences](https://mlsanity.com/paper/2005.12564/) (2020)
- [Kernels over Sets of Finite Sets using RKHS Embeddings, with Application to Bayesian (Combinatorial) Optimization](https://mlsanity.com/paper/1910.04086/) (2019)
- [Higher-order Quasi-Monte Carlo Training of Deep Neural Networks](https://mlsanity.com/paper/2009.02713/) (2020)
- [Message-Passing Monte Carlo: Generating low-discrepancy point sets via Graph Neural Networks](https://mlsanity.com/paper/2405.15059/) (2024)
- [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)
- [Bayesian Optimization with Approximate Set Kernels](https://mlsanity.com/paper/1905.09780/) (2019)
- [Optimizing Kernel Discrepancies via Subset Selection](https://mlsanity.com/paper/2511.02706/) (2025)

## Abstract (arXiv)

Low-discrepancy designs play a central role in quasi-Monte Carlo methods and are increasingly influential in other domains such as machine learning, robotics and computer graphics, to name a few. In recent years, one such low-discrepancy construction method called subset selection has received a lot of attention. Given a large population, one optimally selects a small low-discrepancy subset with respect to a discrepancy-based objective. Versions of this problem are known to be NP-hard. In this text, we establish, for the first time, that the subset selection problem with respect to kernel discrepancies is also NP-hard. Motivated by this intractability, we propose a Bayesian Optimization procedure for the subset selection problem utilizing the recent notion of deep embedding kernels. We demonstrate the performance of the BO algorithm to minimize discrepancy measures and note that the framework is broadly applicable any design criteria.