Problem
Research questions and friction points this paper is trying to address.
Two-sample testing
Generative transport
Distribution comparison
Jensen-Shannon divergence
Two-Sample Testing via Generative Processes
🤖 AI Summary
This study addresses two-sample distribution testing, where existing methods struggle to simultaneously achieve theoretical optimality and finite-sample reliability. We propose a novel framework based on symmetric stochastic interpolation that leverages time-reversal invariance to compute the Jensen-Shannon divergence between marginal distributions for hypothesis testing. The method requires no model training, guarantees exact finite-sample level control via permutation calibration, and achieves adaptivity through multi-scale noise fusion. Theoretically, it attains the minimax optimal separation rate. Empirically, its performance matches or exceeds state-of-the-art kernel-based two-sample tests, establishing a new paradigm for high-dimensional distribution testing that combines statistical rigor with computational efficiency.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Two-Sample Testing
Stochastic Interpolant
Generative Transport
Permutation Calibration
Minimax Separation Rate
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