Spatio-temporal DeepKriging for Interpolation and Probabilistic Forecasting
This provides a scalable solution for large-scale spatio-temporal prediction in environmental monitoring, though it is incremental as it adapts existing deep learning techniques to a known bottleneck.
The authors tackled the problem of spatio-temporal interpolation and forecasting for non-Gaussian, nonstationary processes by proposing a deep neural network-based two-stage model, achieving computational efficiency and eliminating the need for covariance function specification compared to traditional Kriging, as demonstrated on over 200,000 PM2.5 data points.
Gaussian processes (GP) and Kriging are widely used in traditional spatio-temporal mod-elling and prediction. These techniques typically presuppose that the data are observed from a stationary GP with parametric covariance structure. However, processes in real-world applications often exhibit non-Gaussianity and nonstationarity. Moreover, likelihood-based inference for GPs is computationally expensive and thus prohibitive for large datasets. In this paper we propose a deep neural network (DNN) based two-stage model for spatio-temporal interpolation and forecasting. Interpolation is performed in the first step, which utilizes a dependent DNN with the embedding layer constructed with spatio-temporal basis functions. For the second stage, we use Long-Short Term Memory (LSTM) and convolutional LSTM to forecast future observations at a given location. We adopt the quantile-based loss function in the DNN to provide probabilistic forecasting. Compared to Kriging, the proposed method does not require specifying covariance functions or making stationarity assumption, and is computationally efficient. Therefore, it is suitable for large-scale prediction of complex spatio-temporal processes. We apply our method to monthly $PM_{2.5}$ data at more than $200,000$ space-time locations from January 1999 to December 2022 for fast imputation of missing values and forecasts with uncertainties.