LOTTERY: New Method for Two-Sample Testing with Imbalanced Data Sizes
Researchers have developed a new statistical testing method called LOTTERY that leverages abundant reference samples to improve detection of distribution differences when query samples are scarce. The method learns reference-dependent representations and combines multiple representation families to identify departures from the reference distribution. This approach is particularly valuable for few-shot settings where sample-size imbalance is severe, offering both theoretical guarantees and practical performance improvements.
The paper introduces LOTTERY, a data-adaptive two-sample testing approach designed for scenarios with significant sample-size imbalance—where many reference samples are available but only a few query samples are present. Rather than treating this imbalance as a limitation, the method leverages abundant reference data to learn representations that capture both global and local structure of the reference distribution. The approach incorporates multiple representation families and uses an uncertainty-guided principle to adaptively weight them based solely on reference samples. Theoretically, the authors establish that the method maintains proper type I error control through permutation-based testing and achieves consistency, with test power converging to one when the representation set includes at least one consistent representation. Empirically, LOTTERY demonstrates strong performance across various benchmarks while preserving type I error control, making it practical for real-world applications with imbalanced data.
What's missing
The paper does not discuss computational complexity or scalability considerations for the method, nor does it provide explicit guidance on how practitioners should select or design representation families for specific application domains.
What different sources said
- arXiv cs.LGCenter
LOTTERY: Learning from Reference-Only Samples in Two-Sample Testing under Size Asymmetry
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