p-Markov Gaussian Processes for Scalable and Expressive Online Bayesian Nonparametric Time Series Forecasting

TL;DR

This paper introduces the pM-GP filter, an online Bayesian time series forecasting model that achieves scalable, constant-time updates and learning, while maintaining high expressiveness through spectral Matern kernels.

Contribution

The pM-GP filter is a novel online Gaussian process model that offers scalable, exact inference without approximations, and leverages expressive spectral Matern kernels.

Findings

Constant time complexity for online forecasting and learning

Capable of approximating any translation-invariant covariance function

Demonstrated superior performance on real-world datasets

Abstract

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.