Mon Oct 13, F. Flechtner
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Gupta, Naveen and Sivananthan, S., 2025. Convergence analysis of regularised Nyström method for functional linear regression. Inverse Problems, 41(4):045005, doi:10.1088/1361-6420/adbfb6.
• from the NASA Astrophysics Data System • by the DOI System •
@ARTICLE{2025InvPr..41d5005G,
author = {{Gupta}, Naveen and {Sivananthan}, S.},
title = "{Convergence analysis of regularised Nystr{\"o}m method for functional linear regression}",
journal = {Inverse Problems},
keywords = {functional linear regression, reproducing kernel Hilbert space, Nystr{\"o}m subsampling, regularization, covariance operator, Mathematics - Statistics Theory, 62R10, 62G20, 65F22},
year = 2025,
month = apr,
volume = {41},
number = {4},
eid = {045005},
pages = {045005},
abstract = "{The functional linear regression model has been widely studied and
utilized for dealing with functional predictors. In this paper,
we study the Nystr{\"o}m subsampling method, a strategy used to
tackle the computational complexities inherent in big data
analytics, especially within the domain of functional linear
regression model in the framework of reproducing kernel Hilbert
space. By adopting a Nystr{\"o}m subsampling strategy, our aim
is to mitigate the computational overhead associated with kernel
methods, which often struggle to scale gracefully with dataset
size. Specifically, we investigate a regularization-based
approach combined with Nystr{\"o}m subsampling for functional
linear regression model, effectively reducing the computational
complexity from [ image ] to [ image ], where [ image ]
represents the size of the observed empirical dataset and [
image ] is the size of subsampled dataset. Notably, we establish
that these methodologies will achieve optimal convergence rates,
provided that the subsampling level is appropriately selected.
We have also demonstrated numerical examples of Nystr{\"o}m
subsampling in the reproducing kernel Hilbert space framework
for the functional linear regression model.}",
doi = {10.1088/1361-6420/adbfb6},
archivePrefix = {arXiv},
eprint = {2410.19312},
primaryClass = {math.ST},
adsurl = {https://ui.adsabs.harvard.edu/abs/2025InvPr..41d5005G},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
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