mlsanityData to 7 Oct 2026

Selective Inference for Hierarchical Clustering

arXiv 2012.02936 ↗First posted 5 Dec 2020stat.ME stat.MLcited by 37

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Abstract (arXiv)

Classical tests for a difference in means control the type I error rate when the groups are defined a priori. However, when the groups are instead defined via clustering, then applying a classical test yields an extremely inflated type I error rate. Notably, this problem persists even if two separate and independent data sets are used to define the groups and to test for a difference in their means. To address this problem, in this paper, we propose a selective inference approach to test for a difference in means between two clusters. Our procedure controls the selective type I error rate by accounting for the fact that the choice of null hypothesis was made based on the data. We describe how to efficiently compute exact p-values for clusters obtained using agglomerative hierarchical clustering with many commonly-used linkages. We apply our method to simulated data and to single-cell RNA-sequencing data.

Key facts. Cited by 37 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Dec 2020.

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Citing papers per year: 2021: 3; 2022: 5; 2023: 6; 2024: 8; 2025: 8; 2026: 7.

37 papers.

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  1. 2022Selective inference for k-means clusteringcited by 21
  2. 2021Tree-Values: selective inference for regression treescited by 15
  3. 2023Data thinning for convolution-closed distributionscited by 12
  4. 2023CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inferencecited by 10
  5. 2023Generalized Data Thinning Using Sufficient Statisticscited by 7
  6. 2023Interpretable Machine Learning for Discovery: Statistical Challenges & Opportunitiescited by 7
  7. 2022Exact Selective Inference with Randomizationcited by 6
  8. 2024Statistical Test for Attention Map in Vision Transformercited by 6
  9. 2024Statistical Test for Anomaly Detections by Variational Auto-Encoderscited by 6
  10. 2022Kernel Biclustering algorithm in Hilbert Spacescited by 3
  11. 2024Statistical Test for Feature Selection Pipelines by Selective Inferencecited by 3
  12. 2024Statistical Test for Auto Feature Engineering by Selective Inferencecited by 3
25 more
  1. 2025Quantifying Statistical Significance of Deep Nearest Neighbor Anomaly Detection via Selective Inferencecited by 3
  2. 2024Decomposing Gaussians with Unknown Covariancecited by 2
  3. 2024Controllable RANSAC-based Anomaly Detection via Hypothesis Testingcited by 2
  4. 2025Change Point Detection in the Frequency Domain with Statistical Reliabilitycited by 2
  5. 2025Unsupervised Machine Learning for Scientific Discovery: Workflow and Best Practicescited by 2
  6. 2025Statistical Inference for Autoencoder-based Anomaly Detection after Representation Learning-based Domain Adaptationcited by 2
  7. 2021Controlling the False Split Rate in Tree-Based Aggregationcited by 1
  8. 2023When Does Bottom-up Beat Top-down in Hierarchical Community Detection?cited by 1
  9. 2023Bounded P-values in Parametric Programming-based Selective Inferencecited by 1
  10. 2024Statistical Test for Diffusion-Based Anomaly Localization via Selective Inferencecited by 1
  11. 2026Weighted Conformal Clusteringcited by 1
  12. 2021Forest Fire Clustering for Single-cell Sequencing with Iterative Label Propagation and Parallelized Monte Carlo Simulationcited by 0
  13. 2022Statistical Inference for the Dynamic Time Warping Distance, with Application to Abnormal Time-Series Detectioncited by 0
  14. 2022Inferring independent sets of Gaussian variables after thresholding correlationscited by 0
  15. 2024Interpretable Clustering with the Distinguishability Criterioncited by 0
  16. 2025Statistical Inference for Clustering-based Anomaly Detectioncited by 0
  17. 2025Flexible Selective Inference with Flow-based Transport Mapscited by 0
  18. 2025Two-cluster testcited by 0
  19. 2025Hierarchical Clustering With Confidencecited by 0
  20. 2026The Condition-Number Principle for Prototype Clusteringcited by 0
  21. 2026Testing hypotheses via orthogonalizationcited by 0
  22. 2026Automatic Statistical Test for Rationally Expressible Algorithms by Selective Inference, with Applications to Feature Selectioncited by 0
  23. 2026Nonparametric Hypothesis Testing of High-dimensional Clustering With Application to Single-cell RNA Datacited by 0
  24. 2026Statistical Testing for Multiple Instance Learning via Selective Inference with Applications to Computational Pathologycited by 0
  25. 2026Post-Anomaly Detection Inference for Deep SVDDcited by 0