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This paper focuses on interpretable additive Gaussian process (GP) regressionand its efficient implementation for large-scale data with a multi-dimensionalgrid structure, as commonly encountered in spatio-temporal analysis. A popularand scalable approach in the GP literature for this type of data exploits theKronecker product structure in the covariance matrix. However, under theexisting methodology, its use is limited to covariance functions with aseparable product structure, which lacks flexibility in modelling and selectinginteraction effects - an important component in many real-life problems. Toaddress these issues, we propose a class of additive GP models constructed byhierarchical ANOVA kernels. Furthermore, we show that how the Kronecker methodcan be extended to the proposed class of models. Our approach allows for easyidentification of interaction effects, straightforward interpretation of bothmain and interaction effects and efficient implementation for large-scale data.The proposed method is applied to analyse NO2 concentrations during theCOVID-19 lockdown in London. Our scalable method enables analysis ofhourly-recorded data collected from 59 different stations across the city,providing additional insights to findings from previous research using daily orweekly averaged data.

Efficient and Interpretable Additive Gaussian Process Regression and  Application to Analysis of Hourly-recorded $\text{NO}_2$ Concentrations in  London