Zero-Flow Two-Sample Tests
cs.LG, stat.ML
Submitted: 2026-07-23
Updated: 2026-09-30
License: http://creativecommons.org/licenses/by/4.0/
The gist: We propose a new approach to two-sample testing for deciding whether two sets of samples are drawn from the same distribution.
Terminology
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.
Sources
- FMMI: Flow Matching Mutual Information Estimation
- Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow
- Revisiting Classifier Two-Sample Tests
- Permutation p-values should never be zero: calculating exact p-values when permutations are randomly drawn
- Midpoint Generative Models
- Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy
- Zero-Flow Encoders
Related papers
- Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
- AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
- Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
- Convergence issues in Relational Concept Analysis based on AOC-posets
- Beliefs Beyond Posteriors: Local-Consistency Optimisation for Bayesian Neural Networks
- Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks