arXiv：cs.LG· Eshant English, Kenji Fukumizu, Taiji Suzuki·· 7 小时前AI 评分34
通过生成过程实现双样本检验
Two-Sample Testing via Generative Processes
AI 导读
研究者提出一种基于生成式传输的双样本检验方法，直接在两组样本间构建随机插值，利用对称调度下时间反射的分布不变性，通过计算 t 与 1-t 时刻边缘分布的 Jensen-Shannon 散度判断两组样本是否同分布。
正文
Abstract:Deciding whether two samples come from the same distribution is a classical problem in statistics, and generative transport offers a new way to approach it. We build a stochastic interpolant directly between the two samples and observe that, for a symmetric schedule, its law is invariant under the time reflection $t \mapsto 1-t$ whenever the two distributions coincide. We therefore test whether the marginals at times t and 1-t agree by computing their Jensen--Shannon divergence. Both marginals are explicit mixtures over all cross-pairs of observations, so nothing is learned, and permutation calibration gives an exact finite-sample level. For Gaussian noise, this divergence equals a time integral that pairs the reflection defects of the velocity field and of the score, so the test compares transport dynamics rather than endpoints alone. With a narrow-plus-broad noise design, the test attains the minimax separation rate n^{-2s/(4s+d)} over bounded, compactly supported densities whose difference has Sobolev smoothness s > 3d/4, with no lower bound on the densities. Fusing a dyadic grid of noise scales through their permutation ranks, without sample splitting, preserves exact level and adapts to unknown s at an iterated-logarithmic cost. Empirically, the test matches or outperforms state-of-the-art kernel two-sample tests.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.08277 [stat.ML] |
| (or arXiv:2610.08277v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.08277 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Eshant English [view email]
[v1]
Tue, 6 Oct 2026 12:48:27 UTC (656 KB)
来源：arXiv：cs.LG · arxiv.org