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 generalises 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. As our main theoretical contribution, we prove that the new test, with a properly calibrated threshold, has a well-controlled type-I error. In the case of 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.

翻译：我们提出一个以内核为基础的相对合适性非参数测试,目的是比较两种模型,这两种模型都可能有未观测到的潜在变量,因此观察到的变量的边际分布是难以控制的。 拟议的测试概括了最近提议的内核斯坦质差异(KSD)测试(Liu等人,2016年,Chwialkowski等人,2016年,Yang等人,2018年)到潜伏变量模型的案例中。 潜伏变量模型比以前处理的完全观察的模型要普通得多。 作为我们的主要理论贡献,我们证明,新测试具有适当校准的阈值,其类型I错误控制得非常严格。 对于低维潜值结构和高度观测的模型来说,我们的测试大大超过基于模型样本的相对最大值差异测试,没有利用潜伏结构。