Dynamic Spatial-Temporal Embedding via Neural Conditional Random Field for Multivariate Time Series Forecasting

How to capture dynamic spatial-temporal dependencies remains an open question in multivariate time series (MTS) forecasting. Although recent advanced spatial-temporal graph neural networks (STGNNs) achieve superior forecasting performance, they either consider pre-defined spatial correlations or simply learn static graphs. Some research has tried to learn many adjacent matrices to reveal time-varying spatial correlations, but they generate discrete graphs which cannot encode evolutionary information and also face computational complexity problem. In this article, we propose two significant plugins to help automatically learn enhanced dynamic spatial-temporal embedding of MTS data: (1) a novel neural conditional random field (CRF) layer. We find that the implicit time-varying spatial dependencies are reflected by the explicit changeable links between edges, and we propose the neural CRF to encode such pairwise changeable evolutionary inter-dependencies; (2) a structure adaptive graph convolution (SAGC) that does not require pre-defined graphs to capture semantically richer spatial correlations. Then, we integrate the neural CRF, SAGC with recurrent neural network to develop a new STGNN paradigm termed Adaptive Spatial-Temporal graph neural network with Conditional Random Field (ASTCRF), which can be trained in an end-to-end fashion. We validate the effectiveness, efficiency, and scalability of ASTCRF on five public benchmark MTS datasets.