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.

翻译：我们提出了一种基于核的非参数相对拟合优度检验方法，其目标是比较两个可能包含未观测潜变量的模型，且观测变量的边际分布无法直接计算。所提出的检验将近期提出的核斯坦因散度检验（Liu等人，2016；Chwialkowski等人，2016；Yang等人，2018）推广至潜变量模型情形——这类模型比先前所处理的完全观测模型具有更广泛的类别。该新检验在适当校准阈值后能有效控制第一类错误。对于具有低维潜结构和高维观测数据的特定模型，我们的检验显著优于基于模型样本且未利用潜结构的相对最大均值差异检验。