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Non-parametric estimation of functions as well as their derivatives by means of local-polynomial regression is a subject that was studied in the literature since the late 1970's.
Consistent nonparametric regression
Charles J Stone · 1977
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Robust locally weighted regression and smoothing scatterplots
William S Cleveland · 1979
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Optimal rates of convergence for nonparametric estimators
Charles J Stone · 1980
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Optimal global rates of convergence for nonparametric regression
Charles J Stone · 1982
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Probability inequalities for sums of bounded random variables
Wassily Hoeffding · 1994
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Multivariate locally weighted least squares regression
David Ruppert and Matthew P Wand · 1994
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The space complexity of approximating the frequency moments
Noga Alon, Yossi Matias, and Mario Szegedy · 1999
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A distribution-free theory of nonparametric regression
László Györfi, Michael Kohler, Adam Krzyzak, Harro Walk, et al · 2002
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Manifold regularization: A geometric framework for learning from labeled and unlabeled examples
Mikhail Belkin, Partha Niyogi, and Vikas Sindhwani · 2006
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Riemannian geometry for the statistical analysis of diffusion tensor data
P Thomas Fletcher and Sarang Joshi · 2007
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Introduction to nonparametric estimation
Alexandre B Tsybakov · 2008
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Nonparametric regression between general riemannian manifolds
Florian Steinke, Matthias Hein, and Bernhard Schölkopf · 2010
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All of statistics: a concise course in statistical inference
Larry Wasserman · 2013
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PCA-based out-of-sample extension for dimensionality reduction
Yariv Aizenbud, Amit Bermanis, and Amir Averbuch · 2015
Later among the works it cites.
Non-asymptotic rates for manifold, tangent space, and curvature estimation
Eddie Aamari and Clément Levrard · 2017
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Approximation of functions over manifolds: A moving least-squares approach
Barak Sober, Yariv Aizenbud, and David Levin · 2017
Later among the works it cites.
Manifold approximation by moving least-squares projection (mmls)
Barak Sober and David Levin · 2019
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Local conformal autoencoder for standardized data coordinates
Erez Peterfreund, Ofir Lindenbaum, Felix Dietrich, Tom Bertalan, Matan Gavish, Ioannis G Kevrekidis, and Ronald R Coifman · 2020
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Manifold reconstruction using tangential delaunay complexes
Jean-Daniel Boissonnat and Arijit Ghosh · 2014
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Multi-view kernel consensus for data analysis
Moshe Salhov, Ofir Lindenbaum, Yariv Aizenbud, Avi Silberschatz, Yoel Shkolnisky, and Amir Averbuch · 2020
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Non-parametric estimation of manifolds from noisy data
Yariv Aizenbud and Barak Sober · 2021
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