  Network regularization is an effective tool for incorporating structural
prior knowledge to learn coherent models over networks, and has yielded
provably accurate estimates in applications ranging from spatial economics to
neuroimaging studies. Recently, there has been an increasing interest in
extending network regularization to the spatio-temporal case to accommodate the
evolution of networks. However, in both static and spatio-temporal cases,
missing or corrupted edge weights can compromise the ability of network
regularization to discover desired solutions. To address these gaps, we propose
a novel approach---{\it discrepancy-aware network regularization} (DANR)---that
is robust to inadequate regularizations and effectively captures model
evolution and structural changes over spatio-temporal networks. We develop a
distributed and scalable algorithm based on the alternating direction method of
multipliers (ADMM) to solve the proposed problem with guaranteed convergence to
global optimum solutions. Experimental results on both synthetic and real-world
networks demonstrate that our approach achieves improved performance on various
tasks, and enables interpretation of model changes in evolving networks.
