Infectious disease forecasting has been a key focus and proved to be crucial in controlling epidemic. A recent trend is to develop forecast-ing models based on graph neural networks (GNNs). However, existing GNN-based methods suffer from two key limitations: (1) Current models broaden receptive fields by scaling the depth of GNNs, which is insuffi-cient to preserve the semantics of long-range connectivity between distant but epidemic related areas. (2) Previous approaches model epidemics within single spatial scale, while ignoring the multi-scale epidemic pat-terns derived from different scales. To address these deficiencies, we devise the Multi-scale Spatio-temporal Graph Neural Network (MSGNN) based on an innovative multi-scale view. To be specific, in the proposed MSGNN model, we first devise a novel graph learning module, which directly captures long-range connectivity from trans-regional epidemic signals and integrates them into a multi-scale graph. Based on the learned multi-scale graph, we utilize a newly designed graph convolution module to exploit multi-scale epidemic patterns. This module allows us to facilitate multi-scale epidemic modeling by mining both scale-shared and scale-specific pat-terns. Experimental results on forecasting new cases of COVID-19 in United State demonstrate the superiority of our method over state-of-arts. Further analyses and visualization also show that MSGNN offers not only accurate, but also robust and interpretable forecasting result.

Signed and directed networks are ubiquitous in real-world applications. However, there has been relatively little work proposing spectral graph neural networks (GNNs) for such networks. Here we introduce a signed directed Laplacian matrix, which we call the magnetic signed Laplacian, as a natural generalization of both the signed Laplacian on signed graphs and the magnetic Laplacian on directed graphs. We then use this matrix to construct a novel efficient spectral GNN architecture and conduct extensive experiments on both node clustering and link prediction tasks. In these experiments, we consider tasks related to signed information, tasks related to directional information, and tasks related to both signed and directional information. We demonstrate that our proposed spectral GNN is effective for incorporating both signed and directional information, and attains leading performance on a wide range of data sets. Additionally, we provide a novel synthetic network model, which we refer to as the Signed Directed Stochastic Block Model, and a number of novel real-world data sets based on lead-lag relationships in financial time series.