# A Kernel Stein Test for Comparing Latent Variable Models

arXiv: https://arxiv.org/abs/1907.00586 · HTML: https://mlsanity.com/paper/1907.00586/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2019.

## Built on by (most cited first, 18 of 18)

- [Kernel Stein Discrepancy Descent](https://mlsanity.com/paper/2105.09994/) (2021)
- [KSD Aggregated Goodness-of-fit Test](https://mlsanity.com/paper/2202.00824/) (2022)
- [Composite Goodness-of-fit Tests with Kernels](https://mlsanity.com/paper/2111.10275/) (2021)
- [Controlling Moments with Kernel Stein Discrepancies](https://mlsanity.com/paper/2211.05408/) (2022)
- [A kernel Stein test of goodness of fit for sequential models](https://mlsanity.com/paper/2210.10741/) (2022)
- [Nested Expectations with Kernel Quadrature](https://mlsanity.com/paper/2502.18284/) (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)
- [The Minimax Lower Bound of Kernel Stein Discrepancy Estimation](https://mlsanity.com/paper/2510.15058/) (2025)
- [Minimax Estimation of Kernel Stein Discrepancy: Trace versus Hilbert-Schmidt Scales](https://mlsanity.com/paper/2607.03367/) (2026)
- [A Stein Goodness of fit Test for Exponential Random Graph Models](https://mlsanity.com/paper/2103.00580/) (2021)
- [Kernel Tests of Equivalence](https://mlsanity.com/paper/2603.10886/) (2026)
- [Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD](https://mlsanity.com/paper/2607.24235/) (2026)
- [Approximate Stein Classes for Truncated Density Estimation](https://mlsanity.com/paper/2306.00602/) (2023)
- [Statistical Inference for Generative Model Comparison](https://mlsanity.com/paper/2501.18897/) (2025)
- [A Pure Hypothesis Test for Inhomogeneous Random Graph Models Based on a Kernelised Stein Discrepancy](https://mlsanity.com/paper/2505.21580/) (2025)
- [Anchor-based Maximum Discrepancy for Relative Similarity Testing](https://mlsanity.com/paper/2510.10477/) (2025)
- [A moment-matching metric for latent variable generative models](https://mlsanity.com/paper/2111.00875/) (2021)
- [Copula-Stein Discrepancy: A Generator-Based Stein Operator for Archimedean Dependence](https://mlsanity.com/paper/2510.24056/) (2025)

## Abstract (arXiv)

We propose a kernel-based nonparametric test of relative goodness of fit, where the goal is to compare two models, both of which may have unobserved latent variables, such that the marginal distribution of the observed variables is intractable. The proposed test generalizes the recently proposed kernel Stein discrepancy (KSD) tests (Liu et al., 2016, Chwialkowski et al., 2016, Yang et al., 2018) to the case of latent variable models, a much more general class than the fully observed models treated previously. The new test, with a properly calibrated threshold, has a well-controlled type-I error. In the case of certain models with low-dimensional latent structure and high-dimensional observations, our test significantly outperforms the relative Maximum Mean Discrepancy test, which is based on samples from the models and does not exploit the latent structure.