# Weighted Conformal Clustering

arXiv: https://arxiv.org/abs/2606.00436 · HTML: https://mlsanity.com/paper/2606.00436/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 34 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 20 of 20)

- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [A Comprehensive Survey on Deep Clustering: Taxonomy, Challenges, and Future Directions](https://mlsanity.com/paper/2206.07579/) (2022)
- [Selective Inference for Hierarchical Clustering](https://mlsanity.com/paper/2012.02936/) (2020)
- [Selective inference for k-means clustering](https://mlsanity.com/paper/2203.15267/) (2022)
- [PAC Prediction Sets Under Label Shift](https://mlsanity.com/paper/2310.12964/) (2023)
- [Bayesian cluster analysis: Point estimation and credible balls](https://mlsanity.com/paper/1505.03339/) (2015)
- [Statistical Significance for Hierarchical Clustering](https://mlsanity.com/paper/1411.5259/) (2014)
- [Search Algorithms and Loss Functions for Bayesian Clustering](https://mlsanity.com/paper/2105.04451/) (2021)
- [Selective inference for clustering with unknown variance](https://mlsanity.com/paper/2301.12999/) (2023)
- [Statistical Significance of Clustering using Soft Thresholding](https://mlsanity.com/paper/1305.5879/) (2013)
- [Multi-level conformal clustering: A distribution-free technique for clustering and anomaly detection](https://mlsanity.com/paper/1910.08105/) (2019)
- [Inference for Clustering: Conformal Sets for Cluster Labels](https://mlsanity.com/paper/2604.03488/) (2026)

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

- [Cluster-Aware Matching via Laplacian Optimal Transport](https://mlsanity.com/paper/2607.16178/) (2026)
- [Honest Physical-Support Inference after Latent Dictionary Learning: Collision Singularities and Minimax Resolution](https://mlsanity.com/paper/2607.16813/) (2026)

## Abstract (arXiv)

Clustering is a central tool for discovering latent structure in unlabeled data; yet modern clustering pipelines often end with a hard assignment of each observation to a cluster without rigorous measures of assignment uncertainty. We propose a novel weighted conformal approach for constructing valid confidence sets for cluster labels. The key difficulty is that the labels available for calibration are not observed ground-truth labels, but synthetic labels produced by a data-dependent clustering algorithm. Our method develops a conformal inference algorithm that corrects the resulting mismatch with the latent target labels through weights by formulating conformal clustering as a conditional label-distribution shift problem. We first derive an oracle procedure that attains finite-sample marginal coverage and then develop a computationally tractable and implementable version using estimated conditional label probabilities and novel augmented calibration. We show that the coverage of the estimated-weight procedure depends on the estimator, giving an explicit bound on the loss relative to the nominal level. Empirical studies demonstrate that the proposed weighted approach offers improvements over the recently proposed split conformal clustering procedure in terms of informative confidence set size, especially in nonlinear and high-dimensional clustering applications.