Efficient Gaussian process based on BFGS updating and logdet approximation

Leithead, W.E. and Zhang, Y. and Leith, D.J.; (2005) Efficient Gaussian process based on BFGS updating and logdet approximation. In: Proceedings of the 16th IFAC World Congress, 2005. UNSPECIFIED, CZE, p. 217. ISBN 978-3-902661-75-3

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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.