Random scaling of quasi-Newton BFGS method to improve the o(N^2)-operation approximation of covariance-matrix inverse in Gaussian process

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Zhang, Y. and Leithead, W.E. and Leith, D. (2007) Random scaling of quasi-Newton BFGS method to improve the o(N^2)-operation approximation of covariance-matrix inverse in Gaussian process. In: IEEE 22nd International Symposium on Intelligent Control, 2007. ISIC 2007., 2007-10-01. (https://doi.org/10.1109/ISIC.2007.4450928)

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Abstract

Gaussian process (GP) is a Bayesian nonparametric regression model, showing good performance in various applications. Similar to other computational models, Gaussian process frequently encounters the matrix-inverse problem during its model-tuning procedure. The matrix inversion is generally of O(N3) operations where N is the matrix dimension. We proposed using the O(N2)-operation quasi-Newton BFGS method to approximate/replace the exact inverse of covariance matrix in the GP context. As inspired during a paper revision, in this paper we show that by using the random-scaling technique, the accuracy and effectiveness of such a BFGS matrix-inverse approximation could be further improved. These random-scaling BFGS techniques could be widely generalized to other machine-learning systems which rely on explicit matrix-inverse.

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