TY - JOUR

T1 - O(N2)-Operation approximation of covariance matrix inverse in Gaussian process regression based on quasi-Newton BFGS method

AU - Leithead, W.E.

AU - Zhang, Yunong

AU - Science Foundation Ireland grant, 00/PI.1/C067 (Funder)

AU - EPSRC, GR/M76379/01 (Funder)

PY - 2007/3/2

Y1 - 2007/3/2

N2 - Gaussian process (GP) is a Bayesian nonparametric regression model, showing good performance in various applications. However, during its model-tuning procedure, the GP implementation suffers from numerous covariance-matrix inversions of expensive O(N3) operations, where N is the matrix dimension. In this article, we propose using the quasi-Newton BFGS O(N2)-operation formula to approximate/replace recursively the inverse of covariance matrix at every iteration. The implementation accuracy is guaranteed carefully by a matrix-trace criterion and by the restarts technique to generate good initial guesses. A number of numerical tests are then performed based on the sinusoidal regression example and the Wiener-Hammerstein identification example. It is shown that by using the proposed implementation, more than 80% O(N3) operations could be eliminated, and a typical speedup of 5-9 could be achieved as compared to the standard maximum-likelihood-estimation (MLE) implementation commonly used in Gaussian process regression.

AB - Gaussian process (GP) is a Bayesian nonparametric regression model, showing good performance in various applications. However, during its model-tuning procedure, the GP implementation suffers from numerous covariance-matrix inversions of expensive O(N3) operations, where N is the matrix dimension. In this article, we propose using the quasi-Newton BFGS O(N2)-operation formula to approximate/replace recursively the inverse of covariance matrix at every iteration. The implementation accuracy is guaranteed carefully by a matrix-trace criterion and by the restarts technique to generate good initial guesses. A number of numerical tests are then performed based on the sinusoidal regression example and the Wiener-Hammerstein identification example. It is shown that by using the proposed implementation, more than 80% O(N3) operations could be eliminated, and a typical speedup of 5-9 could be achieved as compared to the standard maximum-likelihood-estimation (MLE) implementation commonly used in Gaussian process regression.

KW - Gaussian process regression

KW - matrix inverse

KW - optimization

KW - O(N2) operations

KW - quasi-Newton BFGS method

U2 - 10.1080/03610910601161298

DO - 10.1080/03610910601161298

M3 - Article

VL - 36

SP - 367

EP - 380

JO - Communications in Statistics - Simulation and Computation

JF - Communications in Statistics - Simulation and Computation

SN - 0361-0918

IS - 2

ER -