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    Risk Convergence of Centered Kernel Ridge Regression with Large Dimensional Data

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    Type
    Conference Paper
    Authors
    Elkhalil, Khalil
    Kammoun, Abla cc
    Zhang, Xiangliang cc
    Alouini, Mohamed-Slim cc
    Al-Naffouri, Tareq Y. cc
    KAUST Department
    Communication Theory Lab
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering Program
    Machine Intelligence & kNowledge Engineering Lab
    Date
    2020-04-09
    Preprint Posting Date
    2019-04-19
    Online Publication Date
    2020-04-09
    Print Publication Date
    2020-05
    Permanent link to this record
    http://hdl.handle.net/10754/660647
    
    Metadata
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    Abstract
    This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call centered kernel ridge regression (CKRR), also known in the literature as kernel ridge regression with offset. This modified technique is obtained by accounting for the bias in the regression problem resulting in the old kernel ridge regression but with centered kernels. The analysis is carried out under the assumption that the data is drawn from a Gaussian distribution and heavily relies on tools from random matrix theory (RMT). Under the regime in which the data dimension and the training size grow infinitely large with fixed ratio and under some mild assumptions controlling the data statistics, we show that both the empirical and the prediction risks converge to a deterministic quantities that describe in closed form fashion the performance of CKRR in terms of the data statistics and dimensions. A key insight of the proposed analysis is the fact that asymptotically a large class of kernels achieve the same minimum prediction risk. This insight is validated with synthetic data.
    Citation
    Elkhalil, K., Kammoun, A., Zhang, X., Alouini, M.-S., & Al-Naffouri, T. Y. (2020). Risk Convergence of Centered Kernel Ridge Regression with Large Dimensional Data. ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). doi:10.1109/icassp40776.2020.9053349
    Publisher
    IEEE
    Journal
    IEEE Transactions on Signal Processing
    Conference/Event name
    ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
    ISBN
    978-1-5090-6632-2
    DOI
    10.1109/ICASSP40776.2020.9053349
    arXiv
    1904.09212
    Additional Links
    https://ieeexplore.ieee.org/document/9053349/
    https://ieeexplore.ieee.org/document/9053349/
    https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9053349
    http://arxiv.org/pdf/1904.09212
    ae974a485f413a2113503eed53cd6c53
    10.1109/ICASSP40776.2020.9053349
    Scopus Count
    Collections
    Preprints; Computer Science Program; Electrical Engineering Program; Communication Theory Lab; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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