# Kernel Tests of Equivalence

arXiv: https://arxiv.org/abs/2603.10886 · HTML: https://mlsanity.com/paper/2603.10886/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 104 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 30 of 30)

- [Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods](https://mlsanity.com/paper/1705.07263/) (2017)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [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)
- [Learning Deep Kernels for Non-Parametric Two-Sample Tests](https://mlsanity.com/paper/2002.09116/) (2020)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [MMD Aggregated Two-Sample Test](https://mlsanity.com/paper/2110.15073/) (2021)
- [Control functionals for Monte Carlo integration](https://mlsanity.com/paper/1410.2392/) (2014)
- [A Linear-Time Kernel Goodness-of-Fit Test](https://mlsanity.com/paper/1705.07673/) (2017)
- [Metrizing Weak Convergence with Maximum Mean Discrepancies](https://mlsanity.com/paper/2006.09268/) (2020)
- [Stein's Method Meets Computational Statistics: A Review of Some Recent Developments](https://mlsanity.com/paper/2105.03481/) (2021)
- [A Test of Relative Similarity For Model Selection in Generative Models](https://mlsanity.com/paper/1511.04581/) (2015)
- [A Finite-Particle Convergence Rate for Stein Variational Gradient Descent](https://mlsanity.com/paper/2211.09721/) (2022)
- [KSD Aggregated Goodness-of-fit Test](https://mlsanity.com/paper/2202.00824/) (2022)
- [A Kernel Stein Test for Comparing Latent Variable Models](https://mlsanity.com/paper/1907.00586/) (2019)
- [Composite Goodness-of-fit Tests with Kernels](https://mlsanity.com/paper/2111.10275/) (2021)
- [Credal Two-Sample Tests of Epistemic Uncertainty](https://mlsanity.com/paper/2410.12921/) (2024)
- [Targeted Separation and Convergence with Kernel Discrepancies](https://mlsanity.com/paper/2209.12835/) (2022)
- [Dimension-agnostic inference using cross U-statistics](https://mlsanity.com/paper/2011.05068/) (2020)
- [A Stein Goodness-of-fit Test for Directional Distributions](https://mlsanity.com/paper/2002.06843/) (2020)
- [Kernelized Stein Discrepancy Tests of Goodness-of-fit for Time-to-Event Data](https://mlsanity.com/paper/2008.08397/) (2020)
- [Informative Features for Model Comparison](https://mlsanity.com/paper/1810.11630/) (2018)
- [A General Method for Calibrating Stochastic Radio Channel Models with Kernels](https://mlsanity.com/paper/2012.09612/) (2020)
- [Robust Kernel Hypothesis Testing under Data Corruption](https://mlsanity.com/paper/2405.19912/) (2024)
- [On the Robustness of Kernel Goodness-of-Fit Tests](https://mlsanity.com/paper/2408.05854/) (2024)
- [Kernel Robust Hypothesis Testing](https://mlsanity.com/paper/2203.12777/) (2022)
- [A High-dimensional Convergence Theorem for U-statistics with Applications to Kernel-based Testing](https://mlsanity.com/paper/2302.05686/) (2023)
- [Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancy](https://mlsanity.com/paper/2304.14762/) (2023)
- [Testing semiparametric model-equivalence hypotheses based on the characteristic function](https://mlsanity.com/paper/2111.00280/) (2021)

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

- [Data Fusion with Distributional Equivalence Test-then-pool](https://mlsanity.com/paper/2603.11867/) (2026)
- [Finite-Probe Total-Variation Certificates for Finite-Basis Drifting Models](https://mlsanity.com/paper/2608.01547/) (2026)

## Abstract (arXiv)

We propose novel kernel-based tests for assessing the equivalence between distributions. Traditional goodness-of-fit testing is inappropriate for concluding the absence of distributional differences, because failure to reject the null hypothesis may simply be a result of lack of test power, also known as the Type-II error. This motivates equivalence testing, which aims to assess the absence of a statistically meaningful effect under controlled error rates. However, existing equivalence tests are either limited to parametric distributions or focus only on specific moments rather than the full distribution. We address these limitations using two kernel-based statistical discrepancies: the kernel Stein discrepancy and the Maximum Mean Discrepancy. The null hypothesis of our proposed tests assumes the candidate distribution differs from the nominal distribution by at least a pre-defined margin, which is measured by these discrepancies. We propose two approaches for computing the critical values of the tests, one using an asymptotic normality approximation, and another based on bootstrapping. Numerical experiments are conducted to assess the performance of these tests.