{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T09:27:07Z","timestamp":1789810027005,"version":"4.0.1"},"reference-count":124,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T00:00:00Z","timestamp":1773360000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"EPSRC Centre for Doctoral Training in Computational Statistics and Data Science: COMPASS","award":["EP\/S023569\/1"],"award-info":[{"award-number":["EP\/S023569\/1"]}]},{"name":"UKRI EPSRC NeST Programme","award":["EP\/X002195\/1"],"award-info":[{"award-number":["EP\/X002195\/1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,4,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The manifold hypothesis is a widely accepted tenet of machine learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold, embedded in high-dimensional space. This phenomenon is observed empirically in many real-world situations, has led to development of a wide range of statistical methods in the last few decades, and has been suggested as a key factor in the success of modern AI technologies. We show that rich and sometimes intricate manifold structure in data can emerge from a generic and remarkably simple statistical model\u2014the latent metric space (LMS) model\u2014via elementary concepts such as latent variables, correlation, and stationarity. This establishes a general statistical explanation for why the manifold hypothesis seems to hold in so many situations. Informed by the LMS model we derive procedures to discover and interpret the geometry of high-dimensional data, and explore hypotheses about the data-generating mechanism. These procedures operate under minimal assumptions and make use of well-known dimension reduction methods and graph-analytic algorithms.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkag055","type":"journal-article","created":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T12:34:46Z","timestamp":1773146086000},"page":"353-385","source":"Crossref","is-referenced-by-count":3,"title":["Statistical exploration of the manifold hypothesis"],"prefix":"10.1093","volume":"88","author":[{"given":"Nick","family":"Whiteley","sequence":"first","affiliation":[{"name":"School of Mathematics, University of Bristol , Bristol BS8 1UG ,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-4831-3361","authenticated-orcid":false,"given":"Annie","family":"Gray","sequence":"additional","affiliation":[{"name":"The Alan Turing Institute , London NW1 2DB ,","place":["United 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