In many real-world applications, data is represented in the form of networks with structures and attributes changing over time. The dynamic changes not only happen at nodes/edges, forming local subnetwork processes, but also eventually influence global states of networks. The need to understand what these local network processes are, how they evolve and consequently govern the progression of global network states has become increasingly important. In this paper, we explore these questions and develop a novel algorithm for mining a succinct set of subnetworks that are predictive and evolve along with the progression of global network states. Our algorithm is designed in the framework of logistic regression that fits a model for multi-states of network samples. Its objective function considers both the spatial network topology and temporal smooth transition between adjacent global network states, and we show that its global optimum solution can be achieved via steepest descent. Extensive experimental analysis on both synthetic and real world datasets demonstrates the effectiveness of our algorithm against competing methods, not only in the prediction accuracy but also in terms of domain relevance of the discovered subnetworks.