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Sanna Passino and Heard's contribution to the discussion of 'Statistical exploration of the manifold hypothesis' by Whiteley et al
File(s)
qkag029.pdf (6.33 MB)
Published version
Author(s)
Sanna Passino, Francesco
Heard, Nicholas A
Type
Journal Article
Abstract
The manifold hypothesis is a widely accepted tenet of machine learning which asserts that nominally highdimensional 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-the latent metric space (LMS) model-via 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 highdimensional 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.
Date Issued
2026-04-01
Date Acceptance
2025-11-05
Citation
Journal of The Royal Statistical Society Series B: Statistical Methodology, 2026, 88 (2), pp.420-421
URI
DOI
ISSN
1369-7412
Publisher
Royal Statistical Society
Start Page
420
End Page
421
Journal / Book Title
Journal of The Royal Statistical Society Series B: Statistical Methodology
Volume
88
Issue
2
Copyright Statement
© The Royal Statistical Society 2026. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https:// creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited
License URL
Identifier
10.1093/jrsssb/qkag055
Publication Status
Published
Date Publish Online
2026-01-13