# From Imbalance to Evidence: Deep Nonparametric Testing for Complex Data under Severe Sample Imbalance

arXiv: https://arxiv.org/abs/2610.12946 · HTML: https://mlsanity.com/paper/2610.12946/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 67 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Builds on (most cited first, 29 of 29)

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- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
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- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- ["Do Anything Now": Characterizing and Evaluating In-The-Wild Jailbreak Prompts on Large Language Models](https://mlsanity.com/paper/2308.03825/) (2023)
- [DeCAF: A Deep Convolutional Activation Feature for Generic Visual Recognition](https://mlsanity.com/paper/1310.1531/) (2013)
- [Deep Long-Tailed Learning: A Survey](https://mlsanity.com/paper/2110.04596/) (2021)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Imbalanced-learn: A Python Toolbox to Tackle the Curse of Imbalanced Datasets in Machine Learning](https://mlsanity.com/paper/1609.06570/) (2016)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [MMD Aggregated Two-Sample Test](https://mlsanity.com/paper/2110.15073/) (2021)
- [Graph Kernels: A Survey](https://mlsanity.com/paper/1904.12218/) (2019)
- [Classification accuracy as a proxy for two sample testing](https://mlsanity.com/paper/1602.02210/) (2016)
- [Classification Logit Two-sample Testing by Neural Networks](https://mlsanity.com/paper/1909.11298/) (2019)
- [On the Use of Random Forest for Two-Sample Testing](https://mlsanity.com/paper/1903.06287/) (2019)
- [Better-Than-Chance Classification for Signal Detection](https://mlsanity.com/paper/1608.08873/) (2016)
- [The Shape of Money Laundering: Subgraph Representation Learning on the Blockchain with the Elliptic2 Dataset](https://mlsanity.com/paper/2404.19109/) (2024)
- [Multiple-Splitting Projection Test for High-Dimensional Mean Vectors](https://mlsanity.com/paper/2110.15480/) (2021)
- [Minimax optimal testing by classification](https://mlsanity.com/paper/2306.11085/) (2023)
- [Power-enhanced simultaneous test of high-dimensional mean vectors and covariance matrices with application to gene-set testing](https://mlsanity.com/paper/2109.15287/) (2021)
- [Fisher's combined probability test for high-dimensional covariance matrices](https://mlsanity.com/paper/2006.00426/) (2020)
- [LOTTERY: Learning from Reference-Only Samples in Two-Sample Testing under Size Asymmetry](https://mlsanity.com/paper/2606.08460/) (2026)

## Abstract (arXiv)

Comparing distributions under severe sample imbalance requires effectively using abundant majority observations while retaining sensitivity to differences involving the smaller sample. This challenge is particularly relevant for complex, non-Euclidean data, such as graphs, whose structural characteristics call for flexible testing procedures. Classifier two-sample tests (C2STs) provide such flexibility, but existing procedures are primarily designed for balanced or comparably sized samples. In this paper, we study C2STs in a highly imbalanced regime, and show that severe sample imbalance may substantially degrade testing performance. Different from conventional imbalanced learning approaches that treat sample imbalance merely as a nuisance for classifier training, we turn it into a source of repeated testing evidence. Building on this insight, we propose an Enhanced Imbalance-Aware Deep Classifier Two-Sample Test (EIAD-C2ST), a classifier-agnostic framework designed for sample imbalance that accommodates diverse data modalities by tailoring classifiers to data structure. For computationally expensive deep classifiers, we further develop a scalable representation-amortized implementation strategy. Theoretically, we establish rigorous guarantees on asymptotic size and characterize conditions for power consistency, allowing the imbalance ratio to diverge. We demonstrate the empirical gains using simulations and an application to blockchain forensics. The results reveal that the majority-sample surplus, when properly leveraged, can be organized into useful statistical evidence, rather than an obstacle, for distributional comparisons with complex data.