mlsanityData to 7 Oct 2026

A Wild Bootstrap for Degenerate Kernel Tests

arXiv 1408.5404 ↗First posted 23 Aug 2014stat.MLcited by 28

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Abstract (arXiv)

A wild bootstrap method for nonparametric hypothesis tests based on kernel distribution embeddings is proposed. This bootstrap method is used to construct provably consistent tests that apply to random processes, for which the naive permutation-based bootstrap fails. It applies to a large group of kernel tests based on V-statistics, which are degenerate under the null hypothesis, and non-degenerate elsewhere. To illustrate this approach, we construct a two-sample test, an instantaneous independence test and a multiple lag independence test for time series. In experiments, the wild bootstrap gives strong performance on synthetic examples, on audio data, and in performance benchmarking for the Gibbs sampler.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Aug 2014.

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Citing papers per year: 2021: 4; 2022: 9; 2023: 2; 2024: 3; 2025: 6; 2026: 4.

28 papers.

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  1. 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splittingcited by 33
  2. 2022Efficient Aggregated Kernel Tests using Incomplete U-statisticscited by 27
  3. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  4. 2024Detecting Machine-Generated Texts by Multi-Population Aware Optimization for Maximum Mean Discrepancycited by 20
  5. 2021Composite Goodness-of-fit Tests with Kernelscited by 16
  6. 2022Sequential Kernelized Independence Testingcited by 15
  7. 2024Practical Kernel Tests of Conditional Independencecited by 13
  8. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  9. 2025Low-Rank Thinningcited by 7
  10. 2025Unveiling and Causalizing CoT: A Causal Pespectivecited by 6
  11. 2025DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testingcited by 6
  12. 2021Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fitcited by 4
16 more
  1. 2025A Unified View of Optimal Kernel Hypothesis Testingcited by 4
  2. 2022AgraSSt: Approximate Graph Stein Statistics for Interpretable Assessment of Implicit Graph Generatorscited by 3
  3. 2023Kernel-based Joint Independence Tests for Multivariate Stationary and Non-stationary Time Seriescited by 3
  4. 2021A Stein Goodness of fit Test for Exponential Random Graph Modelscited by 2
  5. 2022Adversarial Attack and Defense for Non-Parametric Two-Sample Testscited by 2
  6. 2022A general framework for the analysis of kernel-based testscited by 2
  7. 2026Regularized f-Divergence Kernel Testscited by 2
  8. 2021Estimating R'enyi's α-Cross-Entropies in a Matrix-Based Waycited by 1
  9. 2022A Kernelised Stein Statistic for Assessing Implicit Generative Modelscited by 1
  10. 2022Non-Parametric Inference of Relational Dependencecited by 1
  11. 2025Probabilistic distances-based hallucination detection in LLMs with RAGcited by 1
  12. 2026Zero-Flow Two-Sample Testscited by 1
  13. 2022Discussion of `Multiscale Fisher's Independence Test for Multivariate Dependence'cited by 0
  14. 2025Testing for Causal Fairnesscited by 0
  15. 2026ProbRes: Volatility Learning for Probabilistic Time-Series Forecastingcited by 0
  16. 2026ASK-NN: An Asymmetric Nearest-Neighbor Test that detects Distribution Drifts in Natural Languagecited by 0