# A fast and effective kernel two-sample test for large-scale data

arXiv: https://arxiv.org/abs/2110.03118 · HTML: https://mlsanity.com/paper/2110.03118/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 56 references that are in the map.
- First posted on arXiv 7 Oct 2021.

## Builds on (most cited first, 16 of 16)

- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods](https://mlsanity.com/paper/1705.07263/) (2017)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [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)
- [Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy](https://mlsanity.com/paper/1611.04488/) (2016)
- [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)
- [A Kernel Two-Sample Test for Functional Data](https://mlsanity.com/paper/2008.11095/) (2020)
- [Two-sample Testing Using Deep Learning](https://mlsanity.com/paper/1910.06239/) (2019)
- [A new graph-based two-sample test for multivariate and object data](https://mlsanity.com/paper/1307.6294/) (2013)
- [Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing](https://mlsanity.com/paper/1508.00655/) (2015)
- [On the Use of Random Forest for Two-Sample Testing](https://mlsanity.com/paper/1903.06287/) (2019)
- [Bayesian Approaches to Distribution Regression](https://mlsanity.com/paper/1705.04293/) (2017)
- [A weighted edge-count two-sample test for multivariate and object data](https://mlsanity.com/paper/1604.06515/) (2016)
- [Generalized Kernel Two-Sample Tests](https://mlsanity.com/paper/2011.06127/) (2020)

## Built on by (most cited first, 2 of 2)

- [Two-sample test based on Self-Organizing Maps](https://mlsanity.com/paper/2212.08960/) (2022)
- [A Semi-Supervised Kernel Two-Sample Test](https://mlsanity.com/paper/2605.01775/) (2026)

## Abstract (arXiv)

Kernel two-sample tests have been widely used, and the development of efficient methods for high-dimensional, large-scale data is receiving increasing attention in the big data era. However, existing methods, such as the maximum mean discrepancy (MMD) and recently proposed kernel-based tests for large-scale data, are computationally intensive and/or ineffective for some common alternatives in high-dimensional data. In this paper, we propose a new test that exhibits high power across a wide range of alternatives. Furthermore, the new test is more robust to high dimensions than existing methods and does not require optimization procedures for choosing kernel bandwidth and other parameters through data splitting. Numerical studies demonstrate that the new approach performs well on both synthetic and real-world data.