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Time-series Gaussian process regression based on toeplitz computation of O(N2) operations and O(N)-level storage

Zhang, Y. and Leithead, W.E. and Leith, D.J. (2005) Time-series Gaussian process regression based on toeplitz computation of O(N2) operations and O(N)-level storage. In: Proceedings of the 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. IEEE, pp. 3711-3716. ISBN 0-7803-9567-0

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Abstract

Gaussian process (GP) regression is a Bayesian nonparametric model showing good performance in various applications. However, its hyperparameter-estimating procedure may contain numerous matrix manipulations of O(N3) arithmetic operations, in addition to the O(N2)-level storage. Motivated by handling the real-world large dataset of 24000 wind-turbine data, we propose in this paper an efficient and economical Toeplitz-computation scheme for time-series Gaussian process regression. The scheme is of O(N2) operations and O(N)-level memory requirement. Numerical experiments substantiate the effectiveness and possibility of using this Toeplitz computation for very large datasets regression (such as, containing 10000~100000 data points).