Multiscale regression on unknown manifolds

Multiscale regression on unknown manifolds

We consider the regression problem of estimating functions on $ \mathbb{R}^D $ but supported on a $ d $-dimensional manifold $ \mathcal{M} ~~\subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear approximation, we construct low-dimensional coordinates o...

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Bibliographic Details
Main Authors: Wenjing Liao, Mauro Maggioni, Stefano Vigogna
Format: Article
Language:English
Published: AIMS Press 2022-06-01
Series:Mathematics in Engineering
Subjects:
manifold learning
polynomial regression
partitioning estimates
adaptive methods
optimal rates
multi-resolution analysis
nonlinear approximation
wavelet thresholding
Online Access:https://www.aimspress.com/article/doi/10.3934/mine.2022028?viewType=HTML

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https://www.aimspress.com/article/doi/10.3934/mine.2022028?viewType=HTML

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