Time-series Gaussian Process Regression Based on Toeplitz Computation of O(N2) Operations and O(N)-level Storage

• Published in: Proceedings of the 44th IEEE Conference on Decision and Control pp. 3711 - 3716
• Main Authors: Yunong Zhang, Leithead, W.E., Leith, D.J.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2005
• Subjects: Acceleration; Aerodynamics; Bayesian methods; Gaussian processes; Maximum likelihood estimation; Noise measurement; Predictive models; Probability distribution; Rotors; Velocity measurement
• ISBN: 9780780395671; 0780395670
• ISSN: 0191-2216
• DOI: 10.1109/CDC.2005.1582739

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(N 3 ) arithmetic operations, in addition to the O(N 2 )-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(N 2 ) 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).