Permutation-free high-order interaction tests
File(s)
Published version (PMLR)
Author(s)
Liu, Z
Peach, RL
Barahona, M
Type
Conference Paper
Abstract
Kernel-based hypothesis tests offer a flexible, non-parametric tool to detect high-order interactions in multivariate data, beyond pairwise relationships. Yet the scalability of such tests is limited by the computationally demanding permutation schemes used to generate null approximations. Here we introduce a family of permutation-free high-order tests for joint independence and partial factorisa-tions of d variables. Our tests eliminate the need for permutation-based approximations by leveraging V-statistics and a novel cross-centring technique to yield test statistics with a standard normal limiting distribution under the null. We present implementations of the tests and showcase their efficacy and scalability through synthetic datasets. We also show applications inspired by causal discovery and feature selection, which highlight both the importance of high-order interactions in data and the need for efficient computational methods.
Date Issued
2025-07-13
Date Acceptance
2025-07-01
Citation
Proceedings of Machine Learning Research, 2025, 267, pp.39244-39260
ISSN
2640-3498
Publisher
MLResearchPress
Start Page
39244
End Page
39260
Journal / Book Title
Proceedings of Machine Learning Research
Volume
267
Copyright Statement
Copyright © The authors and PMLR 2026.
Source
42nd International Conference on Machine Learning
Publication Status
Published
Start Date
2025-07-13
Finish Date
2025-07-19
Coverage Spatial
Vancouver, Canada