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Identifiability of covariance kernels in the Gaussian process regression model
Journal of the Korean Data & Information Science Society 2021;32:1373-92
Published online November 30, 2021;
© 2021 Korean Data and Information Science Society.

Jae Hoan Kim1 · Jaeyong Lee2

1Department of Mechanical Engineering, Seoul National University
2Department of Statistics, Seoul National University
Correspondence to: 1 Undergraduate Student, Department of Mechanical Engineering, Seoul National University, Gwanak, Seoul 08826, Korea.
2 Professor, Department of Statistics, Seoul National University, Gwanak, Seoul 08826, Korea. E-mail:
Jaeyong Lee was supported by the National Research Foundation of Korea (NRF) grants funded by the Korean government (MSIT) (No. 2018R1A2A3074973 and 2020R1A4A1018207).
Received August 11, 2021; Revised September 24, 2021; Accepted September 28, 2021.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Gaussian process regression (GPR) model is a popular nonparametric regression model. In GPR, features of the regression function such as varying degrees of smoothness and periodicities are modeled through combining various covarinace kernels, which are supposed to model certain effects (Bousquet et al., 2011; Gelman et al., 2013). The covariance kernels have unknown parameters which are estimated by the EM-algorithm or Markov Chain Monte Carlo. The estimated parameters are keys to the inference of the features of the regression functions, but identifiability of these parameters has not been investigated. In this paper, we prove identifiability of covariance kernel parameters in two radial basis mixed kernel GPR and radial basis and periodic mixed kernel GPR. We also provide some examples about non-identifiable cases in such mixed kernel GPRs.
Keywords : Covariance, Gaussian Process, Identi ability, Kernel, Regression.