A Kernel Stein Test for Comparing Latent Variable Models
Abstract
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.
Cite
@article{arxiv.1907.00586,
title = {A Kernel Stein Test for Comparing Latent Variable Models},
author = {Heishiro Kanagawa and Wittawat Jitkrittum and Lester Mackey and Kenji Fukumizu and Arthur Gretton},
journal= {arXiv preprint arXiv:1907.00586},
year = {2023}
}
Comments
This is a pre-copyedited, author-produced version of an article accepted for publication in The Journal of the Royal Statistical Society Series: B following peer review