LOTTERY: Learning from Reference-Only Samples in Two-Sample Testing under Size Asymmetry

• URL: http://arxiv.org/abs/2606.08460v1
• Date: Sun, 07 Jun 2026 05:49:42 GMT
• Title: LOTTERY: Learning from Reference-Only Samples in Two-Sample Testing under Size Asymmetry
• Abstract summary: We show how a severe sample-size imbalance can be leveraged constructively.<n>We incorporate a collection of representation families that capture both global and local structure.<n>As the sample sizes grow, the test power converges to one whenever the representation set contains at least one consistent representation.
• Score: 6.903548360333296
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Data-adaptive two-sample testing assesses if two samples come from the same distribution, using a discrepancy learned from the data (e.g., via kernel-based feature representations). Such methods typically rely on data splitting to decouple learning from testing and control type I error. However, this paradigm is ill-suited to few-shot settings with severe sample-size imbalance: abundant reference samples are available, while only a handful of query samples arrive. In this paper, we show how this imbalance can be leveraged constructively. Using abundant reference data, we learn reference-dependent representations that summarize salient structure of the reference distribution and provide informative signals for detecting departures. We incorporate a collection of representation families that capture both global and local structure, and adaptively weight them using only reference samples via an uncertainty-guided principle. Theoretically, we establish permutation-based type I error control and show consistency of the aggregated test: as the sample sizes grow, the test power converges to one whenever the representation set contains at least one consistent representation. Empirically, our aggregation achieves strong performance across a range of benchmarks while retaining type I error control.

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