Sparse Structure Enabled Grid Spectral Mixture Kernel for Temporal Gaussian Process Regression

Feng Yin, Xinwei He, Lishuo Pan, Tianshi Chen, Zhi Quan Tom Luo, Sergios Theodoridis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

We propose a modified spectral mixture (SM) kernel that serves as a universal stationary kernel for temporal Gaussian process regression (GPR). The kernel is named grid spectral mixture (GSM) kernel as we fix the frequency and variance parameters in the original SM kernel to a set of pre-selected grid points. The hyper-parameters are the non-negative weights of all sub-kernel functions and the resulting optimization task falls under the difference-of-convex programming. Due to the nice structure of the optimization problem, the hyper-parameters are solved by an efficient majorization-minimization method instead of the gradient descent methods. It turns out that the solution is sparse, which provides us with a principled guideline to identify the important frequency components of the data. Experimental results based on various classic time series data sets corroborate that the proposed GPR with GSM kernel significantly outperforms the GPR with SM kernel in terms of both the mean-squared-error (MSE) and the stability of the optimization algorithm.

Original languageEnglish (US)
Title of host publication2018 21st International Conference on Information Fusion, FUSION 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages47-54
Number of pages8
ISBN (Print)9780996452762
DOIs
StatePublished - Sep 5 2018
Event21st International Conference on Information Fusion, FUSION 2018 - Cambridge, United Kingdom
Duration: Jul 10 2018Jul 13 2018

Publication series

Name2018 21st International Conference on Information Fusion, FUSION 2018

Other

Other21st International Conference on Information Fusion, FUSION 2018
CountryUnited Kingdom
CityCambridge
Period7/10/187/13/18

Bibliographical note

Funding Information:
Feng Yin is funded by the Shenzhen Science and Technology Innovation Council with the grant number JCYJ20170307155957688 and JCYJ20170411102101881 and partly by the Shenzhen Fundamental Research Fund under Grant No. KQTD2015033114415450.

Keywords

  • Gaussian process
  • difference-of-convex programming
  • grid spectral mixture (GSM) kernel
  • hyperparameter optimization
  • sparse structure
  • temporal data modeling

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