# Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancy

arXiv: https://arxiv.org/abs/2304.14762 · HTML: https://mlsanity.com/paper/2304.14762/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 63 references that are in the map.
- First posted on arXiv 28 Apr 2023.

## Builds on (most cited first, 24 of 24)

- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (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)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [MMD Aggregated Two-Sample Test](https://mlsanity.com/paper/2110.15073/) (2021)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [A Linear-Time Kernel Goodness-of-Fit Test](https://mlsanity.com/paper/1705.07673/) (2017)
- [Blindness of score-based methods to isolated components and mixing proportions](https://mlsanity.com/paper/2008.10087/) (2020)
- [Stein's Method Meets Computational Statistics: A Review of Some Recent Developments](https://mlsanity.com/paper/2105.03481/) (2021)
- [Measuring Sample Quality with Diffusions](https://mlsanity.com/paper/1611.06972/) (2016)
- [Spread Divergence](https://mlsanity.com/paper/1811.08968/) (2018)
- [Sliced Kernelized Stein Discrepancy](https://mlsanity.com/paper/2006.16531/) (2020)
- [A Framework for Adaptive MCMC Targeting Multimodal Distributions](https://mlsanity.com/paper/1812.02609/) (2018)
- [KSD Aggregated Goodness-of-fit Test](https://mlsanity.com/paper/2202.00824/) (2022)
- [The Barker proposal: combining robustness and efficiency in gradient-based MCMC](https://mlsanity.com/paper/1908.11812/) (2019)
- [Towards Healing the Blindness of Score Matching](https://mlsanity.com/paper/2209.07396/) (2022)
- [Controlling Moments with Kernel Stein Discrepancies](https://mlsanity.com/paper/2211.05408/) (2022)
- [The reproducing Stein kernel approach for post-hoc corrected sampling](https://mlsanity.com/paper/2001.09266/) (2020)
- [Gaussian-binary Restricted Boltzmann Machines on Modeling Natural Image Statistics](https://mlsanity.com/paper/1401.5900/) (2014)
- [A fresh take on 'Barker dynamics' for MCMC](https://mlsanity.com/paper/2012.09731/) (2020)
- [Active Slices for Sliced Stein Discrepancy](https://mlsanity.com/paper/2102.03159/) (2021)
- [A Repelling-Attracting Metropolis Algorithm for Multimodality](https://mlsanity.com/paper/1601.05633/) (2016)

## Built on by (most cited first, 4 of 4)

- [Energy Discrepancies: A Score-Independent Loss for Energy-Based Models](https://mlsanity.com/paper/2307.06431/) (2023)
- [On the Robustness of Kernel Goodness-of-Fit Tests](https://mlsanity.com/paper/2408.05854/) (2024)
- [Kernel Tests of Equivalence](https://mlsanity.com/paper/2603.10886/) (2026)
- [Correcting Mode Proportion Bias in Generalized Bayesian Inference via a Weighted Kernel Stein Discrepancy](https://mlsanity.com/paper/2503.02108/) (2025)

## Abstract (arXiv)

Kernelized Stein discrepancy (KSD) is a score-based discrepancy widely used in goodness-of-fit tests. It can be applied even when the target distribution has an unknown normalising factor, such as in Bayesian analysis. We show theoretically and empirically that the KSD test can suffer from low power when the target and the alternative distributions have the same well-separated modes but differ in mixing proportions. We propose to perturb the observed sample via Markov transition kernels, with respect to which the target distribution is invariant. This allows us to then employ the KSD test on the perturbed sample. We provide numerical evidence that with suitably chosen transition kernels the proposed approach can lead to substantially higher power than the KSD test.