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Convergence analysis of regularised Nyström method for functional linear regression

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.

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@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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