An online Bayesian filtering framework for Gaussian process regression: Application to global surface temperature analysis

Over the past centuries, global warming has gradually become one of the most significant issues in our life. Hence, it is crucial to analyze global surface temperature with an efficient and accurate model. Gaussian process (GP) is a popular nonparametric model, due to the power of Bayesian inference framework. However, the performance of GP is often deteriorated for large-scale data sets such as global surface temperature. In this work, we propose a novel online Bayesian filtering framework for large-scale GP regression. There are three contributions. Firstly, we develop a novel GP-based state space model to efficiently process data in a sequential manner. Secondly, based on our state space model, we design a marginalized particle filter to infer the latent function values and learn the model parameters online. It can efficiently reduce the computation burden of GP while improving the estimation accuracy in a recursive Bayesian inference framework. Finally, we successfully apply our approach to a number of synthetic data sets and the large-scale global surface temperature data set. The results show that our approach outperforms related GP variants, and it is an efficient and accurate expert system for global surface temperature analysis.