Speaker
Martina Scolamiero, KTH Royal Institut of Technology
Abstract
The variety hypothesis states that high–dimensional data often concentrates near a low–dimensional manifold. This idea has been widely explored and leveraged in data analysis and machine learning. A formalisation and a statistical test to verify the manifold hypothesis first appeared in work of Fefferman and coauthors [1]. Assuming that data lies close to an algebraic variety can however be quite restrictive, as singularities or stratified structures are often known to be present in data spaces. In this talk I will present the main ideas from [2] where we define a quantitative framework to decide if a probability measure on the unit disk is supported near a real algebraic variety, therefore generalizing the work of [1] to a broader class of spaces. Joint with A. Lerario, P. Roos Hoefgeest and A. Tamai.
[1] Charles Fefferman, Sanjoy Mitter, and Hariharan Narayanan. Testing the manifold hypothesis. J. Amer. Math. Soc., 29(4):983–1049, 2016.
[2] Testing the variety hypothesis. A Lerario, PR Hoefgeest, M Scolamiero, A Tamai arXiv preprint arXiv:2507.16705, 2025.