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)


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
Number of pages1
Publication statusPublished - 8 Jul 2005
Event16th IFAC World Congress Conference - Prague, Czech Republic
Duration: 4 Jul 20058 Jul 2005


Conference16th IFAC World Congress Conference
Country/TerritoryCzech Republic


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


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