For many spatio-temporal applications, building regression models that can reproduce the true data distribution is often as important as building models with high prediction accuracy. For example, knowing the future distribution of daily temperature and precipitation can help scientists determine their long-term trends and assess their potential impact on human and natural systems. As conventional methods are designed to minimize residual errors, the shape of their predicted distribution may not be consistent with their actual distribution. To overcome this challenge, this paper presents a novel, distribution-preserving multi-task learning framework for multi-location prediction of spatio-temporal data. The framework employs a non-parametric density estimation approach with L2-distance to measure the divergence between the predicted and true distribution of the data. Experimental results using climate data from more than 1500 weather stations in the United States show that the proposed framework reduces the distribution error for more than 78% of the stations without degrading the prediction accuracy significantly.

In climate and environmental sciences, vast amount of spatio-temporal data have been generated at varying spatial resolutions from satellite observations and computer models. Integrating such diverse sources of data has proven to be useful for building prediction models as the multi-scale data may capture different aspects of the Earth system. In this paper, we present a novel framework called MUSCAT for predictive modeling of multi-scale, spatio-temporal data. MUSCAT performs a joint decomposition of multiple tensors from different spatial scales, taking into account the relationships between the variables. The latent factors derived from the joint tensor decomposition are used to train the spatial and temporal prediction models at different scales for each location. The outputs from these ensemble of spatial and temporal models will be aggregated to generate future predictions. An incremental learning algorithm is also proposed to handle the massive size of the tensors. Experimental results on real-world data from the United States Historical Climate Network (USHCN) showed that MUSCAT outperformed other competing methods in more than 70\% of the locations.