零流双样本检验
Zero-Flow Two-Sample Tests
- University of Bristol（布里斯托大学）
- RIKEN AIP（理化学研究所先进智能项目中心）
- University of Tokyo（东京大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该论文提出零流双样本检验新方法，基于零流准则构建ZFD，通过分离见证学习与假设评估，利用灵活神经网络并保持统计校准，开发两种学习见证的方法，实验证明其在结构化分布变化检验中能力强且I型错误校准良好。
AI中文摘要：
我们提出一种用于判定两组样本是否来自同一分布的双样本检验新方法。该检验基于零流准则构建统计差异，即零流差异（ZFD）。我们证明了ZFD的有效性并提出实用检验程序，即零流双样本检验（ZF2ST）。关键是了解两个分布的样本如何局部不对齐，并将所得方向模式用作分布差异的证据。通过分离见证学习和假设评估，ZF2ST能使用灵活神经网络并保持有效统计校准。我们开发了基于回归和功率最大化的方法来学习见证。在合成和图像数据集上的实验表明，ZF2ST能在保持良好校准的I型错误的同时，对结构化分布变化实现强大的检验能力。
英文摘要：
Motivated by the success of modern flow-based generative models in modeling complex data, we study two-sample testing through the lens of flow-based methods. We propose the Zero-Flow Two-Sample Test (ZF2ST), built on the zero-flow criterion, which characterizes distributional equality through a time-reversal antisymmetry of a learnable velocity field. We extend this criterion and further develop the Zero-Flow Discrepancy, an identifying discrepancy that controls the Wasserstein distance, and derive a variational representation in terms of a witness function. This representation naturally leads to a witness-based test whose power is governed by the signal-to-noise ratio (SNR), allowing direct power maximization for witness learning. ZF2ST learns the witness on one data split and performs testing on held-out samples, thereby maintaining Type-I error control and admitting a simple asymptotic null distribution. Experimentally, ZF2ST performs competitively across various synthetic and real-world benchmarks, while showing particularly strong performance in distinguishing image distributions from different sources.
