MTSNet: deep probabilistic cross-multivariate time series modeling with external factors for COVID-19

Complex intelligent systems such as for tackling the COVID-19 pandemic involve multiple multivariate time series (MTSs), where both target variables (such as COVID-19 infected, confirmed, and recovered cases) and external factors (such as virus mutation and infectivity, vaccination, and government intervention influence) are coupled. Forecasting such MTSs with multiple external MTS factors needs to model both within and between MTS interactions and handle their uncertainty, heterogeneity, and dynamics. Existing shallow to deep MTS modelers, including regressors, deep recurrent neural networks such as DeepAR, deep state space models, and deep factor models, do not jointly characterize these issues in a probabilistic manner across MTSs. We propose an end-to-end deep probabilistic cross-MTS learning network MTSNet. MTSNet incorporates a tensor input with scaled target and external MTSs. It then vertically and horizontally stacks long-short memory networks for encoding and decoding target MTSs and enhances uncertainty modeling, generalization and forecasting robustness by residual connection, variational zoneout, and probabilistic forecasting. The tensor input is projected to a probability distribution for target MTS forecasting. MTSNet outperforms the SOTA deep probabilistic MTS networks in forecasting COVID-19 confirmed cases and ICU patient numbers for six countries by involving virus mutation, vaccination, government interventions, and infectivity.