Efficient Gaussian process based on BFGS updating and logdet approximation

W.E. Leithead, Y. Zhang, D.J. Leith

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

5 Citations (Scopus)

Abstract

Gaussian process (GP) is a Bayesian nonparametric regression model, showing good performance in various applications. However, its hyperparameterestimation procedure suffers from numerous covariance-matrix inversions of prohibitively O(N3) operations. In this paper, we propose using the quasi-Newton BFGS O(N2)-operation formula to update recursively the inverse of covariance matrix at every iteration. As for the involved log det computation, a power-series expansion based approximation and compensation scheme is proposed with only 50N2 operations. A number of numerical tests are performed based on the 2D- sinusoidal regression example and the Wiener-Hammerstein identification example. It is shown that by using the proposed implementation, more than 80% O(N3) operations are eliminated, and the speedup of 5 - 9 can be achieved.
Original languageEnglish
Title of host publicationProceedings of the 16th IFAC World Congress, 2005
Pages217-217
Number of pages1
Volume16
DOIs
Publication statusPublished - 8 Jul 2005
Event16th IFAC World Congress Conference - Prague, Czech Republic
Duration: 4 Jul 20058 Jul 2005

Conference

Conference16th IFAC World Congress Conference
CountryCzech Republic
CityPrague
Period4/07/058/07/05

Keywords

  • Gaussian process regression
  • compensation
  • approximation
  • power series expansion
  • matrix inverse

Fingerprint Dive into the research topics of 'Efficient Gaussian process based on BFGS updating and logdet approximation'. Together they form a unique fingerprint.

  • Cite this

    Leithead, W. E., Zhang, Y., & Leith, D. J. (2005). Efficient Gaussian process based on BFGS updating and logdet approximation. In Proceedings of the 16th IFAC World Congress, 2005 (Vol. 16, pp. 217-217) https://doi.org/10.3182/20050703-6-CZ-1902.00218