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

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).