Testing the variety hypothesis

Fuente: arXiv
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Autori principali: Lerario, A., Hoefgeest, P. Roos, Scolamiero, M., Tamai, A.
Natura: Preprint
Pubblicazione: 2025
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author Lerario, A.
Hoefgeest, P. Roos
Scolamiero, M.
Tamai, A.
author_facet Lerario, A.
Hoefgeest, P. Roos
Scolamiero, M.
Tamai, A.
contents Given a probability measure on the unit disk, we study the problem of deciding whether, for some threshold probability, this measure is supported near a real algebraic variety of given dimension and bounded degree. We call this "testing the variety hypothesis". We prove an upper bound on the so-called "sample complexity" of this problem and show how it can be reduced to a semialgebraic decision problem. This is done by studying in a quantitative way the Hausdorff geometry of the space of real algebraic varieties of a given dimension and degree.
format Preprint
id arxiv_https___arxiv_org_abs_2507_16705
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Testing the variety hypothesis
Lerario, A.
Hoefgeest, P. Roos
Scolamiero, M.
Tamai, A.
Algebraic Geometry
Metric Geometry
Statistics Theory
Machine Learning
Given a probability measure on the unit disk, we study the problem of deciding whether, for some threshold probability, this measure is supported near a real algebraic variety of given dimension and bounded degree. We call this "testing the variety hypothesis". We prove an upper bound on the so-called "sample complexity" of this problem and show how it can be reduced to a semialgebraic decision problem. This is done by studying in a quantitative way the Hausdorff geometry of the space of real algebraic varieties of a given dimension and degree.
title Testing the variety hypothesis
topic Algebraic Geometry
Metric Geometry
Statistics Theory
Machine Learning
url https://arxiv.org/abs/2507.16705