# E-Valuating Classifier Two-Sample Tests

arXiv: https://arxiv.org/abs/2210.13027 · HTML: https://mlsanity.com/paper/2210.13027/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 61 references that are in the map.
- First posted on arXiv 24 Oct 2022.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Learning Deep Kernels for Non-Parametric Two-Sample Tests](https://mlsanity.com/paper/2002.09116/) (2020)
- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [Interpretable Distribution Features with Maximum Testing Power](https://mlsanity.com/paper/1605.06796/) (2016)
- [Fast Two-Sample Testing with Analytic Representations of Probability Measures](https://mlsanity.com/paper/1506.04725/) (2015)
- [Active MR k-space Sampling with Reinforcement Learning](https://mlsanity.com/paper/2007.10469/) (2020)
- [Universal Inference](https://mlsanity.com/paper/1912.11436/) (2019)
- [Classification accuracy as a proxy for two sample testing](https://mlsanity.com/paper/1602.02210/) (2016)
- [Experimental design for MRI by greedy policy search](https://mlsanity.com/paper/2010.16262/) (2020)
- [Nonparametric Two-Sample Testing by Betting](https://mlsanity.com/paper/2112.09162/) (2021)
- [Two-sample Testing Using Deep Learning](https://mlsanity.com/paper/1910.06239/) (2019)
- [Classification Logit Two-sample Testing by Neural Networks](https://mlsanity.com/paper/1909.11298/) (2019)
- [Sequential Nonparametric Testing with the Law of the Iterated Logarithm](https://mlsanity.com/paper/1506.03486/) (2015)
- [On learning adaptive acquisition policies for undersampled multi-coil MRI reconstruction](https://mlsanity.com/paper/2203.16392/) (2022)
- [Model-X Sequential Testing for Conditional Independence via Testing by Betting](https://mlsanity.com/paper/2210.00354/) (2022)
- [Anytime Valid Tests of Conditional Independence Under Model-X](https://mlsanity.com/paper/2209.12637/) (2022)
- [Interactive rank testing by betting](https://mlsanity.com/paper/2009.05892/) (2020)
- [Exact Anytime-valid Confidence Intervals for Contingency Tables and Beyond](https://mlsanity.com/paper/2203.09785/) (2022)
- [Sharp finite-sample concentration of independent variables](https://mlsanity.com/paper/2008.13293/) (2020)
- [Predictive Independence Testing, Predictive Conditional Independence Testing, and Predictive Graphical Modelling](https://mlsanity.com/paper/1711.05869/) (2017)

## Built on by (most cited first, 10 of 10)

- [Sequential Predictive Two-Sample and Independence Testing](https://mlsanity.com/paper/2305.00143/) (2023)
- [L-C2ST: Local Diagnostics for Posterior Approximations in Simulation-Based Inference](https://mlsanity.com/paper/2306.03580/) (2023)
- [A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Science](https://mlsanity.com/paper/2403.12636/) (2024)
- [On Continuous Monitoring of Risk Violations under Unknown Shift](https://mlsanity.com/paper/2506.16416/) (2025)
- [Deep anytime-valid hypothesis testing](https://mlsanity.com/paper/2310.19384/) (2023)
- [Keeping Medical AI Healthy and Trustworthy: A Review of Detection and Correction Methods for System Degradation](https://mlsanity.com/paper/2506.17442/) (2025)
- [Active Sequential Two-Sample Testing](https://mlsanity.com/paper/2301.12616/) (2023)
- [Simulation-based Inference with the Generalized Kullback-Leibler Divergence](https://mlsanity.com/paper/2310.01808/) (2023)
- [Detecting Performance Degradation under Data Shift in Pathology Vision-Language Model](https://mlsanity.com/paper/2601.00716/) (2026)
- [Sequential Kernel-based Conditional Independence Testing via Adaptive Betting](https://mlsanity.com/paper/2606.18993/) (2026)

## Abstract (arXiv)

We introduce a powerful deep classifier two-sample test for high-dimensional data based on E-values, called E-value Classifier Two-Sample Test (E-C2ST). Our test combines ideas from existing work on split likelihood ratio tests and predictive independence tests. The resulting E-values are suitable for anytime-valid sequential two-sample tests. This feature allows for more effective use of data in constructing test statistics. Through simulations and real data applications, we empirically demonstrate that E-C2ST achieves enhanced statistical power by partitioning datasets into multiple batches beyond the conventional two-split (training and testing) approach of standard classifier two-sample tests. This strategy increases the power of the test while keeping the type I error well below the desired significance level.