Explainable Spatio-Temporal Forecasting with Shape Functions

Xianbin Cao, Vy Vo, Tingjin Chu, Guoqi Qian, Mingming Gong

Keywords: Spatio-temporal Forecasting, Shape Function, Spatial Weight Matrix

TL;DR: The shape functions, being learnable and restricted by shape constraints, are expected to capture spatial variability or distance-based effects over distance.

Abstract: Spatio-temporal modelling and forecasting are challenging due to their complicated spatial dependence, temporal dynamics, and scenarios. Many statistical models, such as Spatial Auto-regression Model (SAR) and Spatial Dynamic Panel Data Model (SDPD), are restricted by a pre-specified spatial weight matrix and thus are limited to reflect its flexibility. Graph-based or convolution-based methods can learn more flexible representations, but they fail to show the exact interactions between locations due to the lack of explainability. This paper proposes a spatial regression model with shape functions to address the limitations of existing methods. Our method learns the shape functions by incorporating shape constraints, which are able to capture spatial variability or distance-based effects over distance. Therefore, our approach enjoys a learnable spatial weight matrix with a distance-based explanation. We demonstrate our method's efficiency and forecasting performance on synthetic and real data.