Distribution Preserving Multi-task Regression for Spatio-Temporal Data

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.