Zero-Flow Two-Sample Tests
2026-07-23 • Machine Learning
Machine Learning
AI summaryⓘ
The authors introduce a new method to test if two groups of samples come from the same source. Their method, called the zero-flow two-sample test (ZF2ST), looks at how the samples misalign locally and uses this pattern to detect differences between distributions. They show the method is reliable and can use neural networks without losing accuracy in deciding if the distributions match. Tests on various data sets show the method works well in finding real differences while avoiding false alarms.
two-sample testingdistribution comparisonzero-flow discrepancy (ZFD)statistical hypothesis testingneural networkstype-I errorwitness functionregressiontest powerdistributional difference
Authors
Yakun Wang, Leyang Wang, Song Liu, Taiji Suzuki
Abstract
We propose a new approach to two-sample testing for deciding whether two sets of samples are drawn from the same distribution. The test is built on a statistical discrepancy based on the zero-flow criterion, termed zero-flow discrepancy (ZFD). We prove the validity of ZFD and propose a practical testing procedure, termed the zero-flow two-sample test (ZF2ST). The key idea is to learn how samples from the two distributions are locally misaligned and use the resulting directional pattern as evidence of distributional difference. By separating witness learning from hypothesis evaluation, ZF2ST can use flexible neural networks while maintaining valid statistical calibration. We develop both regression-based and power-maximized approaches for learning the witness. Experiments on synthetic and image datasets demonstrate that ZF2ST can achieve strong testing power for structured distributional changes while maintaining well-calibrated type-I error.