  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 -- the Latent Metric 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 Latent Metric
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, scaleable graph-analytic algorithms.
