# Learning Kernel Tests Without Data Splitting

arXiv: https://arxiv.org/abs/2006.02286 · HTML: https://mlsanity.com/paper/2006.02286/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2020.

## Built on by (most cited first, 19 of 19)

- [MMD Aggregated Two-Sample Test](https://mlsanity.com/paper/2110.15073/) (2021)
- [MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting](https://mlsanity.com/paper/2306.08777/) (2023)
- [Efficient Aggregated Kernel Tests using Incomplete U-statistics](https://mlsanity.com/paper/2206.09194/) (2022)
- [A Witness Two-Sample Test](https://mlsanity.com/paper/2102.05573/) (2021)
- [KSD Aggregated Goodness-of-fit Test](https://mlsanity.com/paper/2202.00824/) (2022)
- [AutoML Two-Sample Test](https://mlsanity.com/paper/2206.08843/) (2022)
- [Meta Two-Sample Testing: Learning Kernels for Testing with Limited Data](https://mlsanity.com/paper/2106.07636/) (2021)
- [Neural Tangent Kernel Maximum Mean Discrepancy](https://mlsanity.com/paper/2106.03227/) (2021)
- [Compress Then Test: Powerful Kernel Testing in Near-linear Time](https://mlsanity.com/paper/2301.05974/) (2023)
- [What Is That Talk About? A Video-to-Text Summarization Dataset for Scientific Presentations](https://mlsanity.com/paper/2502.08279/) (2025)
- [Boosting the Power of Kernel Two-Sample Tests](https://mlsanity.com/paper/2302.10687/) (2023)
- [A Bias-Variance-Covariance Decomposition of Kernel Scores for Generative Models](https://mlsanity.com/paper/2310.05833/) (2023)
- [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)
- [Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit](https://mlsanity.com/paper/2106.12105/) (2021)
- [Learning Representations for Independence Testing](https://mlsanity.com/paper/2409.06890/) (2024)
- [Collaborative likelihood-ratio estimation over graphs](https://mlsanity.com/paper/2205.14461/) (2022)
- [Towards Practicable Sequential Shift Detectors](https://mlsanity.com/paper/2307.14758/) (2023)
- [Learning Majority-to-Minority Transformations with MMD and Triplet Loss for Imbalanced Classification](https://mlsanity.com/paper/2509.11511/) (2025)

## Abstract (arXiv)

Modern large-scale kernel-based tests such as maximum mean discrepancy (MMD) and kernelized Stein discrepancy (KSD) optimize kernel hyperparameters on a held-out sample via data splitting to obtain the most powerful test statistics. While data splitting results in a tractable null distribution, it suffers from a reduction in test power due to smaller test sample size. Inspired by the selective inference framework, we propose an approach that enables learning the hyperparameters and testing on the full sample without data splitting. Our approach can correctly calibrate the test in the presence of such dependency, and yield a test threshold in closed form. At the same significance level, our approach's test power is empirically larger than that of the data-splitting approach, regardless of its split proportion.