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This work addresses a critical gap in few-shot two-sample testing by constructing a method that leverages abundant reference data to detect distributional shifts in severely imbalanced query scenarios. Theoretically grounded in permutation-based error control and empirically validated across benchmarks, the approach adaptively aggregates diverse representation families to maximize detection power without compromising statistical rigor. For practitioners dealing with limited query samples, this technique offers a robust framework for anomaly detection and distributional comparison where traditional data-splitting paradigms fail.
LOTTERY: Learning from Reference-Only Samples in Two-Sample Testing under Size Asymmetry
arXiv:2606.08460v1 Announce Type: cross 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2606.08460 [stat.ML]
(or arXiv:2606.08460v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2606.08460 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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