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dc.contributor.authorElkhalil, Khalil
dc.contributor.authorKammoun, Abla
dc.contributor.authorZhang, Xiangliang
dc.contributor.authorAlouini, Mohamed-Slim
dc.contributor.authorAl-Naffouri, Tareq Y.
dc.date.accessioned2019-12-18T05:50:02Z
dc.date.available2019-12-18T05:50:02Z
dc.date.issued2020
dc.identifier.citationElkhalil, K., Kammoun, A., Zhang, X., Alouini, M., & Al-Naffouri, T. (2020). Risk Convergence of Centered Kernel Ridge Regression with Large Dimensional Data. IEEE Transactions on Signal Processing, 1–1. doi:10.1109/tsp.2020.2975939
dc.identifier.doi10.1109/TSP.2020.2975939
dc.identifier.urihttp://hdl.handle.net/10754/660647
dc.description.abstractThis 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. Inspired by this theoretical result, we subsequently build a consistent estimator of the prediction risk based on the training data which allows to optimally tune the design parameters. 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 both synthetic and real data.
dc.description.sponsorshipThis work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award OSR-CRG2019-4041.
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)
dc.relation.urlhttps://ieeexplore.ieee.org/document/9018066/
dc.relation.urlhttps://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9018066
dc.rightsThis is the submitted version of an article later published in IEEE Transactions on Signal Processing. (c) 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
dc.subjectKernel regression
dc.subjectcentered kernels
dc.subjectrandom matrix theory
dc.titleRisk Convergence of Centered Kernel Ridge Regression with Large Dimensional Data
dc.typeArticle
dc.contributor.departmentElectrical Engineering Program
dc.contributor.departmentPhysical Science and Engineering (PSE) Division
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentComputer Science Program
dc.identifier.journalIEEE Transactions on Signal Processing
dc.eprint.versionPre-print
dc.contributor.institutionDuke University,Department of Electrical and Computer Engineering,Durham,NC,27707
dc.identifier.arxivid1904.09212
kaust.personElkhalil, Khalil
kaust.personKammoun, Abla
kaust.personZhang, Xiangliang
kaust.personAlouini, Mohamed-Slim
kaust.personAl-Naffouri, Tareq Y.
kaust.grant.numberOSR-CRG2019-4041
refterms.dateFOA2019-12-18T05:50:36Z
kaust.acknowledged.supportUnitOffice of Sponsored Research (OSR)
dc.date.published-online2020-04-09
dc.date.published-print2020-05
dc.date.posted2019-04-19


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