LOTTERY: New method uses reference-only samples for accurate two-sample testing

Traditional two-sample testing often relies on data splitting to separate learning from testing, which fails when query samples are few. LOTTERY flips this paradigm: instead of treating sample imbalance as a limitation, it leverages the abundant reference data to build rich representations. The method learns a family of reference-dependent representations that summarize salient structure (e.g., kernel embeddings for global features and local density estimates). These representations are then adaptively weighted using only reference samples via an uncertainty-guided principle, so that the most informative features dominate the test statistic.

On the theoretical side, LOTTERY provides two key guarantees: permutation-based type I error control and consistency as sample sizes grow. If at least one representation family is consistent (i.e., can distinguish the distributions), the aggregated test power converges to one. Empirically, the method outperforms baselines on a range of benchmarks (e.g., synthetic shifts, real-world domain shifts) while strictly controlling false positives. The approach is particularly useful in few-shot settings common in anomaly detection, medical diagnostics, and online monitoring.

For professionals working with imbalanced datasets, LOTTERY offers a principled way to detect distribution shifts without requiring large query samples. Its theoretical rigor ensures reliability, and its adaptive weighting makes it robust across different types of changes. The paper is accepted at ICML 2026, signaling strong peer validation.