{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T15:00:14Z","timestamp":1788361214952,"version":"build-2803163510"},"reference-count":84,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,5,6]],"date-time":"2023-05-06T00:00:00Z","timestamp":1683331200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,7,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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., Proceedings of the 33rd international conference on machine learning (pp. 276\u2013284); Chwialkowski et al., (2016), In Proceedings of the 33rd international conference on machine learning (pp. 2606\u20132615); Yang et al., (2018), In Proceedings of the 35th international conference on machine learning (pp. 5561\u20135570)) 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 structures 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.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkad050","type":"journal-article","created":{"date-parts":[[2023,5,6]],"date-time":"2023-05-06T06:21:05Z","timestamp":1683354065000},"page":"986-1011","source":"Crossref","is-referenced-by-count":3,"title":["A kernel Stein test for comparing latent variable models"],"prefix":"10.1093","volume":"85","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7556-8827","authenticated-orcid":false,"given":"Heishiro","family":"Kanagawa","sequence":"first","affiliation":[{"name":"Gatsby Computational Neuroscience Unit, University College London , London , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wittawat","family":"Jitkrittum","sequence":"additional","affiliation":[{"name":"Empirical Inference, Max Planck Institute for Intelligent Systems , T\u00fcbingen , Germany"},{"name":"Google Research , New York, NY , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lester","family":"Mackey","sequence":"additional","affiliation":[{"name":"Microsoft Research New England , Cambridge, MA , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kenji","family":"Fukumizu","sequence":"additional","affiliation":[{"name":"The Institute of Statistical Mathematics , Tachikawa, Tokyo , Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arthur","family":"Gretton","sequence":"additional","affiliation":[{"name":"Gatsby Computational Neuroscience Unit, University College London , London , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,5,6]]},"reference":[{"key":"2023071211415118400_qkad050-B1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1201\/b17520","volume-title":"Handbook of mixed membership models and their applications","author":"Airoldi","year":"2014"},{"issue":"3","key":"2023071211415118400_qkad050-B2","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1090\/S0002-9947-1950-0051437-7","article-title":"Theory of reproducing kernels","volume":"68","author":"Aronszajn","year":"1950","journal-title":"Transactions of the American Mathematical Society"},{"issue":"A","key":"2023071211415118400_qkad050-B3","doi-asserted-by":"crossref","first-page":"175","DOI":"10.2307\/3214155","article-title":"Stein\u2019s method and Poisson process convergence","volume":"25","author":"Barbour","year":"1988","journal-title":"Journal of Applied Probability"},{"key":"2023071211415118400_qkad050-B4","author":"Barp","year":"2019"},{"key":"2023071211415118400_qkad050-B5","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316894","volume-title":"Statistical factor analysis and related methods","author":"Basilevsky","year":"1994"},{"issue":"4","key":"2023071211415118400_qkad050-B6","first-page":"591","article-title":"Comments on \u2019Representations of knowledge in complex systems\u2019 by U. 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