New test compares distributions using generative transport dynamics
Two-Sample Testing via Generative Processes
Machine Learning
Summary
Deciding if two groups of data come from the same source is a common statistical problem. The authors create a method that looks at how one sample can be smoothly changed into the other and checks if this process looks the same when reversed in time. This approach tests differences in the data beyond just their endpoints, helping detect subtle changes. Their method works well even with complicated data shapes and matches or beats existing popular tests.
What this means in practice
- •For data science teams: Validate if two datasets come from the same distribution using a test that compares transformation dynamics, improving detection of subtle differences.
- •For quality assurance teams: Check if outputs from two production processes match statistically by comparing the dynamics of data transformations rather than just endpoint measurements.
Authors
Eshant English, Kenji Fukumizu, Taiji Suzuki
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.