mlsanityData to 7 Oct 2026

Selective inference for k-means clustering

arXiv 2203.15267 ↗First posted 29 Mar 2022stat.ME stat.MLcited by 21

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Abstract (arXiv)

We consider the problem of testing for a difference in means between clusters of observations identified via k-means clustering. In this setting, classical hypothesis tests lead to an inflated Type I error rate. To overcome this problem, we take a selective inference approach. We propose a finite-sample p-value that controls the selective Type I error for a test of the difference in means between a pair of clusters obtained using k-means clustering, and show that it can be efficiently computed. We apply our proposal in simulation, and on hand-written digits data and single-cell RNA-sequencing data.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 34 of its 104 references that are in the map. First posted on arXiv 29 Mar 2022.

Builds on

34 of 104 references.

References · 34

  1. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,841
  2. 2014Statistical guarantees for the EM algorithm: From population to sample-based analysiscited by 131
  3. 2013Exact post-selection inference, with application to the lassocited by 90
  4. 2014Optimal Inference After Model Selectioncited by 63
  5. 2016Statistical and Computational Guarantees of Lloyd's Algorithm and its Variantscited by 52
  6. 2014Exact Post-Selection Inference for Sequential Regression Procedurescited by 47
  7. 2015Robust Covariance and Scatter Matrix Estimation under Huber's Contamination Modelcited by 47
  8. 2019Optimality of Spectral Clustering in the Gaussian Mixture Modelcited by 42
  9. 2020Selective Inference for Hierarchical Clusteringcited by 37
  10. 2017Valid Inference Corrected for Outlier Removalcited by 25
  11. 2019Testing for a Change in Mean After Changepoint Detectioncited by 25
  12. 2020Computing Valid p-value for Optimal Changepoint by Selective Inference using Dynamic Programmingcited by 25
22 more
  1. 2021More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programmingcited by 24
  2. 2018More powerful post-selection inference, with application to the Lassocited by 22
  3. 2016Selective Inference for Group-Sparse Linear Modelscited by 21
  4. 2015Regularized EM Algorithms: A Unified Framework and Statistical Guaranteescited by 19
  5. 2018Post-Selection Inference for Changepoint Detection Algorithms with Application to Copy Number Variation Datacited by 19
  6. 2014A significance test for forward stepwise model selectioncited by 17
  7. 2021Splitting strategies for post-selection inferencecited by 14
  8. 2014Influential Feature PCA for high dimensional clusteringcited by 13
  9. 2015Selective inference in regression models with groups of variablescited by 9
  10. 2014Statistical Significance for Hierarchical Clusteringcited by 8
  11. 2017Unifying approach to selective inference with applications to cross-validationcited by 8
  12. 2017Permutation methods for factor analysis and PCAcited by 7
  13. 2020Scientific intuition inspired by machine learning generated hypothesescited by 7
  14. 2020Finite mixture models do not reliably learn the number of componentscited by 6
  15. 2021More powerful selective inference for the graph fused lassocited by 6
  16. 2020Multicarving for high-dimensional post-selection inferencecited by 5
  17. 2020Selective Inference for Latent Block Modelscited by 3
  18. 2017Sparse covariance matrix estimation in high-dimensional deconvolutioncited by 2
  19. 2019Statistical Methods for Replicability Assessmentcited by 2
  20. 2020Selective Inference for Additive and Linear Mixed Modelscited by 2
  21. 2013Statistical significance of variables driving systematic variationcited by 1
  22. 2021Quantifying uncertainty in spikes estimated from calcium imaging datacited by 1

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Citing papers per year: 2022: 2; 2023: 4; 2024: 3; 2025: 5; 2026: 7.

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  1. 2023CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inferencecited by 10
  2. 2023Generalized Data Thinning Using Sufficient Statisticscited by 7
  3. 2024Efficient Sparse PCA via Block-Diagonalizationcited by 4
  4. 2022Kernel Biclustering algorithm in Hilbert Spacescited by 3
  5. 2025Quantifying Statistical Significance of Deep Nearest Neighbor Anomaly Detection via Selective Inferencecited by 3
  6. 2025Change Point Detection in the Frequency Domain with Statistical Reliabilitycited by 2
  7. 2025Statistical Inference for Autoencoder-based Anomaly Detection after Representation Learning-based Domain Adaptationcited by 2
  8. 2023Bounded P-values in Parametric Programming-based Selective Inferencecited by 1
  9. 2024Adaptively Robust and Sparse K-means Clusteringcited by 1
  10. 2026Weighted Conformal Clusteringcited by 1
  11. 2022Inferring independent sets of Gaussian variables after thresholding correlationscited by 0
  12. 2023Unsupervised Learning of Phylogenetic Trees via Split-Weight Embeddingcited by 0
9 more
  1. 2024Interpretable Clustering with the Distinguishability Criterioncited by 0
  2. 2025Two-cluster testcited by 0
  3. 2025Hierarchical Clustering With Confidencecited by 0
  4. 2026The Condition-Number Principle for Prototype Clusteringcited by 0
  5. 2026Drawing Lines in Psychological Space: What K-means Clustering Reveals in Simulated and Real Psychometric Datacited by 0
  6. 2026Testing hypotheses via orthogonalizationcited by 0
  7. 2026Automatic Statistical Test for Rationally Expressible Algorithms by Selective Inference, with Applications to Feature Selectioncited by 0
  8. 2026Nonparametric Hypothesis Testing of High-dimensional Clustering With Application to Single-cell RNA Datacited by 0
  9. 2026Statistical Testing for Multiple Instance Learning via Selective Inference with Applications to Computational Pathologycited by 0