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

arXiv: https://arxiv.org/abs/2606.08460 · HTML: https://mlsanity.com/paper/2606.08460/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 48 references that are in the map.
- First posted on arXiv 7 Jun 2026.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift](https://mlsanity.com/paper/1810.11953/) (2018)
- [On the (Statistical) Detection of Adversarial Examples](https://mlsanity.com/paper/1702.06280/) (2017)
- [Learning Deep Kernels for Non-Parametric Two-Sample Tests](https://mlsanity.com/paper/2002.09116/) (2020)
- [Explainable Deep One-Class Classification](https://mlsanity.com/paper/2007.01760/) (2020)
- [DROCC: Deep Robust One-Class Classification](https://mlsanity.com/paper/2002.12718/) (2020)
- [Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy](https://mlsanity.com/paper/1611.04488/) (2016)
- [MMD Aggregated Two-Sample Test](https://mlsanity.com/paper/2110.15073/) (2021)
- [Deep One-Class Classification via Interpolated Gaussian Descriptor](https://mlsanity.com/paper/2101.10043/) (2021)
- [Interpretable Distribution Features with Maximum Testing Power](https://mlsanity.com/paper/1605.06796/) (2016)
- [Maximum Mean Discrepancy Test is Aware of Adversarial Attacks](https://mlsanity.com/paper/2010.11415/) (2020)
- [Classification accuracy as a proxy for two sample testing](https://mlsanity.com/paper/1602.02210/) (2016)
- [MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting](https://mlsanity.com/paper/2306.08777/) (2023)
- [A Witness Two-Sample Test](https://mlsanity.com/paper/2102.05573/) (2021)
- [Detecting Machine-Generated Texts by Multi-Population Aware Optimization for Maximum Mean Discrepancy](https://mlsanity.com/paper/2402.16041/) (2024)
- [CADet: Fully Self-Supervised Out-Of-Distribution Detection With Contrastive Learning](https://mlsanity.com/paper/2210.01742/) (2022)
- [A Unified Data Representation Learning for Non-parametric Two-sample Testing](https://mlsanity.com/paper/2412.00613/) (2024)
- [DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testing](https://mlsanity.com/paper/2510.11140/) (2025)
- [H2ST: Hierarchical Two-Sample Tests for Continual Out-of-Distribution Detection](https://mlsanity.com/paper/2503.14832/) (2025)
- [Anchor-based Maximum Discrepancy for Relative Similarity Testing](https://mlsanity.com/paper/2510.10477/) (2025)

## Built on by (most cited first, 1 of 1)

- [From Imbalance to Evidence: Deep Nonparametric Testing for Complex Data under Severe Sample Imbalance](https://mlsanity.com/paper/2610.12946/) (2026)

## Abstract (arXiv)

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.