# A general framework for the analysis of kernel-based tests

arXiv: https://arxiv.org/abs/2209.00124 · HTML: https://mlsanity.com/paper/2209.00124/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 39 references that are in the map.
- First posted on arXiv 31 Aug 2022.

## Builds on (most cited first, 12 of 12)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [MMD Aggregated Two-Sample Test](https://mlsanity.com/paper/2110.15073/) (2021)
- [A Wild Bootstrap for Degenerate Kernel Tests](https://mlsanity.com/paper/1408.5404/) (2014)
- [Efficient Aggregated Kernel Tests using Incomplete U-statistics](https://mlsanity.com/paper/2206.09194/) (2022)
- [KSD Aggregated Goodness-of-fit Test](https://mlsanity.com/paper/2202.00824/) (2022)
- [The Weighted Generalised Covariance Measure](https://mlsanity.com/paper/2111.04361/) (2021)
- [Kernelized Stein Discrepancy Tests of Goodness-of-fit for Time-to-Event Data](https://mlsanity.com/paper/2008.08397/) (2020)
- [A Reproducing Kernel Hilbert Space log-rank test for the two-sample problem](https://mlsanity.com/paper/1904.05187/) (2019)
- [A kernel log-rank test of independence for right-censored data](https://mlsanity.com/paper/1912.03784/) (2019)
- [A Multiple kernel testing procedure for non-proportional hazards in factorial designs](https://mlsanity.com/paper/2206.07239/) (2022)

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

- [Practical Kernel Tests of Conditional Independence](https://mlsanity.com/paper/2402.13196/) (2024)
- [The Third Pillar of Causal Analysis? A Measurement Perspective on Causal Representations](https://mlsanity.com/paper/2505.17708/) (2025)

## Abstract (arXiv)

Kernel-based tests provide a simple yet effective framework that use the theory of reproducing kernel Hilbert spaces to design non-parametric testing procedures. In this paper we propose new theoretical tools that can be used to study the asymptotic behaviour of kernel-based tests in several data scenarios, and in many different testing problems. Unlike current approaches, our methods avoid using lengthy U and V statistics expansions and limit theorems, that commonly appear in the literature, and works directly with random functionals on Hilbert spaces. Therefore, our framework leads to a much simpler and clean analysis of kernel tests, only requiring mild regularity conditions. Furthermore, we show that, in general, our analysis cannot be improved by proving that the regularity conditions required by our methods are both sufficient and necessary. To illustrate the effectiveness of our approach we present a new kernel-test for the conditional independence testing problem, as well as new analyses for already known kernel-based tests.