Risk Convergence of Centered Kernel Ridge Regression with Large Dimensional Data
dc.contributor.author | Elkhalil, Khalil | |
dc.contributor.author | Kammoun, Abla | |
dc.contributor.author | Zhang, Xiangliang | |
dc.contributor.author | Alouini, Mohamed-Slim | |
dc.contributor.author | Al-Naffouri, Tareq Y. | |
dc.date.accessioned | 2019-12-18T05:50:02Z | |
dc.date.available | 2019-12-18T05:50:02Z | |
dc.date.issued | 2020 | |
dc.identifier.citation | Elkhalil, 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.doi | 10.1109/TSP.2020.2975939 | |
dc.identifier.uri | http://hdl.handle.net/10754/660647 | |
dc.description.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. 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.sponsorship | This work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award OSR-CRG2019-4041. | |
dc.publisher | Institute of Electrical and Electronics Engineers (IEEE) | |
dc.relation.url | https://ieeexplore.ieee.org/document/9018066/ | |
dc.relation.url | https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9018066 | |
dc.rights | This 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.subject | Kernel regression | |
dc.subject | centered kernels | |
dc.subject | random matrix theory | |
dc.title | Risk Convergence of Centered Kernel Ridge Regression with Large Dimensional Data | |
dc.type | Article | |
dc.contributor.department | Electrical Engineering Program | |
dc.contributor.department | Physical Science and Engineering (PSE) Division | |
dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division | |
dc.contributor.department | Computer Science Program | |
dc.identifier.journal | IEEE Transactions on Signal Processing | |
dc.eprint.version | Pre-print | |
dc.contributor.institution | Duke University,Department of Electrical and Computer Engineering,Durham,NC,27707 | |
dc.identifier.arxivid | 1904.09212 | |
kaust.person | Elkhalil, Khalil | |
kaust.person | Kammoun, Abla | |
kaust.person | Zhang, Xiangliang | |
kaust.person | Alouini, Mohamed-Slim | |
kaust.person | Al-Naffouri, Tareq Y. | |
kaust.grant.number | OSR-CRG2019-4041 | |
refterms.dateFOA | 2019-12-18T05:50:36Z | |
kaust.acknowledged.supportUnit | Office of Sponsored Research (OSR) | |
dc.date.published-online | 2020-04-09 | |
dc.date.published-print | 2020-05 | |
dc.date.posted | 2019-04-19 |
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