Spatio-temporal deep kernel Gaussian process for state prediction with time series measurements

State prediction from noisy time series measurements is a challenging task found in areas like intelligent transport, structural health monitoring, and environmental monitoring. This paper proposes a Spatio-Temporal Deep Kernel Gaussian Process (STDK GP) approach, which leverages the feature extraction capabilities of convolutional neural networks with the uncertainty quantification of Gaussian Process (GP) methods. The model features a composite spatio-temporal kernel that operates on learned deep features. A key aspect of our approach is that this kernel is learned end-to-end with the feature extractor, allowing it to effectively capture complex spatial and temporal patterns and enabling robust uncertainty quantification. Evaluated on a real-world vehicular traffic forecasting task, the proposed STDK GP demonstrates superior performance. Specifically, it achieves a root mean square error of 2.67105 km/h and improves prediction accuracy by approximately 15.28% over the standard GP approach, 21.23% over the state-of-the-art structural recurrent neural network and by more than 53% over stand-alone deep neural networks.