p-Markov Gaussian Processes for Scalable and Expressive Online Bayesian Nonparametric Time Series Forecasting
This addresses scalability issues in time series forecasting for applications requiring efficient online processing, though it is incremental as it builds on Gaussian process regression with spectral Matern kernels.
The paper tackles the problem of scalable online Bayesian nonparametric time series forecasting by introducing the pM-GP filter, which achieves constant time and memory complexity for online forecasting and hyperparameter learning without approximations, and demonstrates benefits on real-life datasets.
In this paper we introduce a novel online time series forecasting model we refer to as the pM-GP filter. We show that our model is equivalent to Gaussian process regression, with the advantage that both online forecasting and online learning of the hyper-parameters have a constant (rather than cubic) time complexity and a constant (rather than squared) memory requirement in the number of observations, without resorting to approximations. Moreover, the proposed model is expressive in that the family of covariance functions of the implied latent process, namely the spectral Matern kernels, have recently been proven to be capable of approximating arbitrarily well any translation-invariant covariance function. The benefit of our approach compared to competing models is demonstrated using experiments on several real-life datasets.