Two-Sample Testing via Generative Processes

Key points

• 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.1
• We therefore test whether the marginals at times t and 1-t agree by computing their Jensen--Shannon divergence.1
• 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.1
• 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.1

Sources (1)

• [1]Two-Sample Testing via Generative Processes
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 6, 12:48 PM

  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.

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