mlsanityData to 7 Oct 2026

Exact Statistical Inference for the Wasserstein Distance by Selective Inference

arXiv 2109.14206 ↗First posted 29 Sep 2021stat.ML cs.LGcited by 7

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Abstract (arXiv)

In this paper, we study statistical inference for the Wasserstein distance, which has attracted much attention and has been applied to various machine learning tasks. Several studies have been proposed in the literature, but almost all of them are based on asymptotic approximation and do not have finite-sample validity. In this study, we propose an exact (non-asymptotic) inference method for the Wasserstein distance inspired by the concept of conditional Selective Inference (SI). To our knowledge, this is the first method that can provide a valid confidence interval (CI) for the Wasserstein distance with finite-sample coverage guarantee, which can be applied not only to one-dimensional problems but also to multi-dimensional problems. We evaluate the performance of the proposed method on both synthetic and real-world datasets.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 21 of its 39 references that are in the map. First posted on arXiv 29 Sep 2021.

Builds on

21 of 39 references.

References · 21

  1. 2015Learning with a Wasserstein Losscited by 194
  2. 2015On Wasserstein Two Sample Testing and Related Families of Nonparametric Testscited by 165
  3. 2013Exact post-selection inference, with application to the lassocited by 90
  4. 2014Optimal Inference After Model Selectioncited by 63
  5. 2014Exact Post-Selection Inference for Sequential Regression Procedurescited by 47
  6. 2017Valid Inference Corrected for Outlier Removalcited by 25
  7. 2020Computing Valid p-value for Optimal Changepoint by Selective Inference using Dynamic Programmingcited by 25
  8. 2019Computing Valid p-values for Image Segmentation by Selective Inferencecited by 24
  9. 2021More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programmingcited by 24
  10. 2018More powerful post-selection inference, with application to the Lassocited by 22
  11. 2016Selective Inference for Group-Sparse Linear Modelscited by 21
  12. 2018Post-Selection Inference for Changepoint Detection Algorithms with Application to Copy Number Variation Datacited by 19
9 more
  1. 2014Selecting the number of principal components: estimation of the true rank of a noisy matrixcited by 18
  2. 2014A significance test for forward stepwise model selectioncited by 17
  3. 2015Selective Sequential Model Selectioncited by 16
  4. 2021Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuationcited by 16
  5. 2021Fast and More Powerful Selective Inference for Sparse High-order Interaction Modelcited by 15
  6. 2015Selective inference in regression models with groups of variablescited by 9
  7. 2016Integrative Methods for Post-Selection Inference Under Convex Constraintscited by 7
  8. 2017On parameter estimation with the Wasserstein distancecited by 7
  9. 2020More Powerful and General Selective Inference for Stepwise Feature Selection using the Homotopy Continuation Approachcited by 6

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Cited by year

Citing papers per year: 2021: 1; 2022: 1; 2023: 3; 2024: 0; 2025: 2.

7 papers.

  1. 2021Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inferencecited by 10
  2. 2023CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inferencecited by 10
  3. 2025Statistical Inference for Autoencoder-based Anomaly Detection after Representation Learning-based Domain Adaptationcited by 2
  4. 2023Tight Non-asymptotic Inference via Sub-Gaussian Intrinsic Moment Normcited by 1
  5. 2023Bounded P-values in Parametric Programming-based Selective Inferencecited by 1
  6. 2022Statistical Inference for the Dynamic Time Warping Distance, with Application to Abnormal Time-Series Detectioncited by 0
  7. 2025Statistical Inference for Clustering-based Anomaly Detectioncited by 0