TY - GEN

T1 - Risk Convergence of Centered Kernel Ridge Regression with Large Dimensional Data

AU - Elkhalil, Khalil

AU - Kammoun, Abla

AU - Zhang, Xiangliang

AU - Alouini, Mohamed-Slim

AU - Al-Naffouri, Tareq Y.

N1 - KAUST Repository Item: Exported on 2021-03-25

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/668256

UR - https://ieeexplore.ieee.org/document/9053349/

UR - http://www.scopus.com/inward/record.url?scp=85089246436&partnerID=8YFLogxK

U2 - 10.1109/ICASSP40776.2020.9053349

DO - 10.1109/ICASSP40776.2020.9053349

M3 - Conference contribution

SN - 978-1-5090-6632-2

SP - 8763

EP - 8767

BT - ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

PB - IEEE

ER -