Efficient Gaussian Process Based on Bfgs Updating and Logdet Approximation

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(N) operations. In this paper, we propose using the quasi-Newton BFGS O(N)-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 50N operations. A number of numerical tests are performed based on the 2Dsinusoidal regression example and the Wiener-Hammerstein identification example. It is shown that by using the proposed implementation, more than 80% O(N ) operations are eliminated, and the speedup of 5 ∼ 9 can be achieved. Copyright c © 2005 IFAC