O(N 2)-Operation Approximation of Covariance Matrix Inverse in Gaussian Process Regression Based on Quasi-Newton BFGS Method |
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Authors: | W E Leithead Yunong Zhang |
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Institution: | 1. Hamilton Institute, National University of Ireland , Maynooth, Ireland w.leithead@eee.strath.ac.uk ynzhang@ieee.org;3. Hamilton Institute, National University of Ireland , Maynooth, Ireland |
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Abstract: | 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. |
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Keywords: | Gaussian process regression Matrix inverse Optimization O(N 2) operations Quasi-Newton BFGS method |
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