# Classification Logit Two-sample Testing by Neural Networks

arXiv: https://arxiv.org/abs/1909.11298 · HTML: https://mlsanity.com/paper/1909.11298/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2019.

## Built on by (most cited first, 26 of 26)

- [Convergence of flow-based generative models via proximal gradient descent in Wasserstein space](https://mlsanity.com/paper/2310.17582/) (2023)
- [A Witness Two-Sample Test](https://mlsanity.com/paper/2102.05573/) (2021)
- [Sequential Predictive Two-Sample and Independence Testing](https://mlsanity.com/paper/2305.00143/) (2023)
- [AutoML Two-Sample Test](https://mlsanity.com/paper/2206.08843/) (2022)
- [Detecting Machine-Generated Texts by Multi-Population Aware Optimization for Maximum Mean Discrepancy](https://mlsanity.com/paper/2402.16041/) (2024)
- [Neural Tangent Kernel Maximum Mean Discrepancy](https://mlsanity.com/paper/2106.03227/) (2021)
- [A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Science](https://mlsanity.com/paper/2403.12636/) (2024)
- [CADet: Fully Self-Supervised Out-Of-Distribution Detection With Contrastive Learning](https://mlsanity.com/paper/2210.01742/) (2022)
- [E-Valuating Classifier Two-Sample Tests](https://mlsanity.com/paper/2210.13027/) (2022)
- [A Data-Driven Approach to Robust Hypothesis Testing Using Sinkhorn Uncertainty Sets](https://mlsanity.com/paper/2202.04258/) (2022)
- [The Representation Jensen-Shannon Divergence](https://mlsanity.com/paper/2305.16446/) (2023)
- [Variable Selection for Kernel Two-Sample Tests](https://mlsanity.com/paper/2302.07415/) (2023)
- [A Unified Data Representation Learning for Non-parametric Two-sample Testing](https://mlsanity.com/paper/2412.00613/) (2024)
- [A Manifold Two-Sample Test Study: Integral Probability Metric with Neural Networks](https://mlsanity.com/paper/2205.02043/) (2022)
- [Neural network-based CUSUM for online change-point detection](https://mlsanity.com/paper/2210.17312/) (2022)
- [Automatic dataset shift identification to support safe deployment of medical imaging AI](https://mlsanity.com/paper/2411.07940/) (2024)
- [Zero-Flow Two-Sample Tests](https://mlsanity.com/paper/2607.21542/) (2026)
- [Kernel-Based Tests for Likelihood-Free Hypothesis Testing](https://mlsanity.com/paper/2308.09043/) (2023)
- [Learning Representations for Independence Testing](https://mlsanity.com/paper/2409.06890/) (2024)
- [Deep Hypothesis Tests Detect Clinically Relevant Subgroup Shifts in Medical Images](https://mlsanity.com/paper/2303.04862/) (2023)
- [Anchor-based Maximum Discrepancy for Relative Similarity Testing](https://mlsanity.com/paper/2510.10477/) (2025)
- [Sparse, self-organizing ensembles of local kernels detect rare statistical anomalies](https://mlsanity.com/paper/2511.03095/) (2025)
- [R-divergence for Estimating Model-oriented Distribution Discrepancy](https://mlsanity.com/paper/2310.01109/) (2023)
- [Are Two Datasets Close Enough With Statistical Significance? A Kernel Distributional Closeness Testing Approach](https://mlsanity.com/paper/2507.12843/) (2025)
- [USAD: Uncertainty-aware Statistical Adversarial Detection](https://mlsanity.com/paper/2606.27832/) (2026)
- [From Imbalance to Evidence: Deep Nonparametric Testing for Complex Data under Severe Sample Imbalance](https://mlsanity.com/paper/2610.12946/) (2026)

## Abstract (arXiv)

The recent success of generative adversarial networks and variational learning suggests training a classifier network may work well in addressing the classical two-sample problem. Network-based tests have the computational advantage that the algorithm scales to large samples. This paper proposes a two-sample statistic which is the difference of the logit function, provided by a trained classification neural network, evaluated on the testing set split of the two datasets. Theoretically, we prove the testing power to differentiate two sub-exponential densities given that the network is sufficiently parametrized. When the two densities lie on or near to low-dimensional manifolds embedded in possibly high-dimensional space, the needed network complexity is reduced to only scale with the intrinsic dimensionality. Both the approximation and estimation error analysis are based on a new result of near-manifold integral approximation. In experiments, the proposed method demonstrates better performance than previous network-based tests using classification accuracy as the two-sample statistic, and compares favorably to certain kernel maximum mean discrepancy tests on synthetic datasets and hand-written digit datasets.