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Stable coresets: Unleashing the power of uniform sampling

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.8Download Report PDF
clustering$k$-mediancoresetsuniform sampling$\ell_1$ metric
Abstract:

Uniform sampling is a highly efficient method for data summarization. However, its effectiveness in producing coresets for clustering problems is not yet well understood, primarily because it generally does not yield a strong coreset, which is the prevailing notion in the literature. We formulate \emph{stable coresets}, a notion that is intermediate between the standard notions of weak and strong coresets, and effectively combines the broad applicability of strong coresets with highly efficient constructions, through uniform sampling, of weak coresets. Our main result is that a uniform sample of size O(ϵ−2log⁡d)O(\epsilon^{-2}\log d) yields, with high constant probability, a stable coreset for 11-median in Rd\mathbb{R}^d under the ℓ1\ell_1 metric. We then leverage the powerful properties of stable coresets to easily derive new coreset constructions, all through uniform sampling, for ℓ1\ell_1 and related metrics, such as Kendall-tau and Jaccard. We also show applications to fair clustering and to approximation algorithms for kk-median problems in these metric spaces. Our experiments validate the benefits of stable coresets in practice, in terms of both construction time and approximation quality.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper introduces stable coresets, a notion intermediate between weak and strong coresets, and demonstrates that uniform sampling of size O(ε⁻²log d) yields stable coresets for 1-median in ℓ₁ metric. Within the taxonomy, it resides in the Sampling-Based Construction Methods leaf under Coreset Construction Techniques and Frameworks. This leaf contains four papers total, including the original work, indicating a moderately populated research direction. The sibling papers explore sensitivity sampling, importance sampling optimality, and uniform sampling power, suggesting active investigation of sampling strategies but not extreme crowding.

The paper's leaf sits within the broader Coreset Construction Techniques and Frameworks branch, which also includes General Coreset Frameworks and Meta-Algorithms (three papers) and Deterministic and Sketch-Based Approaches (three papers). Neighboring branches address Euclidean clustering objectives (k-means, k-median, generalized clustering) and specialized variants (robust, fair, projective clustering). The scope note for Sampling-Based Construction Methods explicitly covers importance, uniform, and sensitivity-based sampling, while excluding non-sampling approaches. The paper's focus on uniform sampling and stability properties connects it to foundational sampling work but diverges by proposing a new coreset notion rather than refining existing sensitivity frameworks.

Among eight candidates examined across three contributions, no clearly refuting prior work was identified. For the stable coresets notion and framework, four candidates were examined with zero refutable matches. The uniform sampling result for 1-median in ℓ₁ examined one candidate with no refutation. The general framework for stable coreset construction examined three candidates, again with no refutable overlap. Given the limited search scope (eight total candidates, not hundreds), these statistics suggest the contributions may occupy relatively unexplored territory within the sampling-based construction space, though exhaustive confirmation would require broader literature coverage.

Based on the limited search of eight semantically related candidates, the work appears to introduce genuinely novel concepts—particularly the stable coreset notion—within an active but not overcrowded research direction. The taxonomy structure shows the paper sits among four sampling-focused works, with clear boundaries separating it from deterministic methods and meta-algorithmic frameworks. However, the small candidate pool examined means this assessment reflects top-K semantic matches rather than comprehensive field coverage, and deeper investigation of the broader clustering coreset literature could reveal additional relevant prior work.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
8
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: coreset construction for clustering problems. The field centers on building small weighted subsets (coresets) that approximate the cost of clustering the full dataset, enabling scalable algorithms for massive data. The taxonomy reveals several major branches: foundational techniques and frameworks (including sampling-based and sensitivity-based methods), specialized constructions for Euclidean objectives (k-means, k-median), variants addressing robustness or fairness constraints, extensions to non-Euclidean and graph metrics, streaming and dynamic settings, distributed and federated scenarios, and empirical studies alongside theoretical surveys. Early works such as Kmeans Kmedian Coresets[34] and Streamkm++[50] established the importance sampling paradigm, while more recent efforts like Improved Euclidean Means[3] and Optimal Euclidean Clustering[12] push toward tighter size bounds and faster construction. Surveys like Coresets Updated Survey[14] and Coresets and Sketches[11] provide overviews of the evolving landscape, and empirical comparisons such as Comparative Coreset Methods[15] and Empirical Kmeans Evaluation[45] assess practical performance across diverse datasets. A particularly active line of work explores sampling-based construction methods, balancing theoretical guarantees with computational efficiency. Sensitivity Sampling[6] and Importance Sampling Optimal[19] refine the classical importance sampling framework, while Uniform Sampling Power[37] investigates simpler uniform schemes. Stable Coresets[0] sits squarely within this sampling-based branch, emphasizing stability properties that ensure consistent approximation quality across different random draws. Its focus contrasts with Sensitivity Sampling[6], which prioritizes sensitivity-driven weights, and with Uniform Sampling Power[37], which explores the surprising effectiveness of uniform sampling under certain conditions. Meanwhile, Practical Coreset Constructions[1] and Lightweight Coresets Initialization[5] address the trade-off between theoretical optimality and real-world scalability, highlighting ongoing questions about how to design coresets that are both provably small and fast to compute in practice.

Claimed Contributions

Stable coresets notion and framework

The authors introduce stable coresets, a new coreset notion that lies between weak and strong coresets. This notion preserves the relative ordering of costs across different centers rather than absolute cost values, enabling efficient construction through uniform sampling while maintaining broad applicability to submetrics similar to strong coresets.

4 retrieved papers
Uniform sampling yields stable coresets for 1-median in l1

The authors prove that uniform sampling produces stable coresets of size O(ε−2 log d) for the 1-median problem in l1 metric spaces with high probability. This establishes a rigorous theoretical foundation for uniform sampling in coreset construction, which was previously viewed primarily as a heuristic method.

1 retrieved paper
General framework for stable coreset construction

The authors develop a general framework applicable to arbitrary metric spaces that establishes sufficient conditions for a subset to be a stable coreset. The framework introduces the concept of relative cost-difference approximation and provides a systematic approach for proving stable coreset properties across different metric spaces.

3 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Stable coresets notion and framework

The authors introduce stable coresets, a new coreset notion that lies between weak and strong coresets. This notion preserves the relative ordering of costs across different centers rather than absolute cost values, enabling efficient construction through uniform sampling while maintaining broad applicability to submetrics similar to strong coresets.

Contribution

Uniform sampling yields stable coresets for 1-median in l1

The authors prove that uniform sampling produces stable coresets of size O(ε−2 log d) for the 1-median problem in l1 metric spaces with high probability. This establishes a rigorous theoretical foundation for uniform sampling in coreset construction, which was previously viewed primarily as a heuristic method.

Contribution

General framework for stable coreset construction

The authors develop a general framework applicable to arbitrary metric spaces that establishes sufficient conditions for a subset to be a stable coreset. The framework introduces the concept of relative cost-difference approximation and provides a systematic approach for proving stable coreset properties across different metric spaces.

Table of Contents

Stable coresets: Unleashing the power of uniform sampling | Novelty Validation