Testing the Manifold Hypothesis¶
Fefferman, C., Mitter, S., & Narayanan, H. (2016). Testing the Manifold Hypothesis. Journal of the American Mathematical Society, 29(4), 983-1049.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Manifold
- In statistics and machine learning the manifold hypothesis — that high-dimensional data lies on or near a much lower-dimensional manifold — is the structural premise of dimensionality reduction, representation learning, and many generative models.
This sourceFormalizes and tests the manifold hypothesis that high-dimensional data lies on or near a much-lower-dimensional manifold.
Supported in partVerified against the publisher's abstract
The abstract states the manifold hypothesis and calls it the basis of manifold learning, but does not name dimensionality reduction, representation learning or generative models.
“The hypothesis that high dimensional data tend to lie in the vicinity of a low dimensional manifold is the basis of manifold learning.”
- In statistics and machine learning the manifold hypothesis — that high-dimensional data lies on or near a much lower-dimensional manifold — is the structural premise of dimensionality reduction, representation learning, and many generative models.
Mechanisms¶
- Manifold Learning Diagnostic
- Its strength is that it puts a falsifiable check in front of the whole archetype — the manifold hypothesis
This sourceDevelops a statistical algorithm that tests whether sampled data are well fit by a low-dimensional manifold.
- Its strength is that it puts a falsifiable check in front of the whole archetype — the manifold hypothesis
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 1 of 2 citations: 1 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
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Registry ID ref:21c2fa887de0 · see in the full table