# A Kernelised Stein Statistic for Assessing Implicit Generative Models

arXiv: https://arxiv.org/abs/2206.00149 · HTML: https://mlsanity.com/paper/2206.00149/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 71 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 30 of 35)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Do CIFAR-10 Classifiers Generalize to CIFAR-10?](https://mlsanity.com/paper/1806.00451/) (2018)
- [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)
- [Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy](https://mlsanity.com/paper/1611.04488/) (2016)
- [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)
- [Interpretable Distribution Features with Maximum Testing Power](https://mlsanity.com/paper/1605.06796/) (2016)
- [Minimum Stein Discrepancy Estimators](https://mlsanity.com/paper/1906.08283/) (2019)
- [Message Passing Stein Variational Gradient Descent](https://mlsanity.com/paper/1711.04425/) (2017)
- [A Linear-Time Kernel Goodness-of-Fit Test](https://mlsanity.com/paper/1705.07673/) (2017)
- [Learning deep kernels for exponential family densities](https://mlsanity.com/paper/1811.08357/) (2018)
- [Stochastic Stein Discrepancies](https://mlsanity.com/paper/2007.02857/) (2020)
- [A Wild Bootstrap for Degenerate Kernel Tests](https://mlsanity.com/paper/1408.5404/) (2014)
- [Nonparametric Score Estimators](https://mlsanity.com/paper/2005.10099/) (2020)

## Built on by (most cited first, 1 of 1)

- [Stein Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2502.03587/) (2025)

## Abstract (arXiv)

Synthetic data generation has become a key ingredient for training machine learning procedures, addressing tasks such as data augmentation, analysing privacy-sensitive data, or visualising representative samples. Assessing the quality of such synthetic data generators hence has to be addressed. As (deep) generative models for synthetic data often do not admit explicit probability distributions, classical statistical procedures for assessing model goodness-of-fit may not be applicable. In this paper, we propose a principled procedure to assess the quality of a synthetic data generator. The procedure is a kernelised Stein discrepancy (KSD)-type test which is based on a non-parametric Stein operator for the synthetic data generator of interest. This operator is estimated from samples which are obtained from the synthetic data generator and hence can be applied even when the model is only implicit. In contrast to classical testing, the sample size from the synthetic data generator can be as large as desired, while the size of the observed data, which the generator aims to emulate is fixed. Experimental results on synthetic distributions and trained generative models on synthetic and real datasets illustrate that the method shows improved power performance compared to existing approaches.